I think a big part of it comes down to how each nation tended to run the local economies and social hierarchies of their overseas empires. In particular, it is how these empires were founded that would set the tone for how they grew and how much that growth relied on immigration from the home country. Bear in mind here, growth is a general term, and all three of these empires were more interested in economic growth over population growth. If one required the other, so be it, but that was not always the case.

In the case of the Spanish colonies, their initial social/economic system was the encomienda system, declared law in 1501 by the Spanish Crown. To put it bluntly, it was a devolved form of feudalism that allowed Spain to incorporate the conquered natives as subjects and grant authority to the encomanderos, the Spanish landowners who were often conquistadores and soldiers. In theory, natives would provide labour and tribute to the encomanderos in exchange for education and protection. In reality, it led to some of the worst atrocities of the colonial era because it allowed the conquerors to be in charge who, if not brutal, were certainly interested in getting rich and not all that concerned about the Crown's laws.

Already, you can see that this social system did not really have Spanish emigration in mind, but rather was an attempt by the Crown to consolidate its power over the massive amount of land and people it had just acquired. The system had plenty of room for new settlers, sure, but it was not reliant on them as there was an easily exploitable workforce already there. So you can see how slave economies are obviously terrible for the slaves, but they are not good for the peasant either. The slaves take the peasant's place and, worse, they require fewer resources. As such, the Spanish populations in the Americas tended to be smaller and more aristocratic.

Even though the encomienda system was abolished and replaced by the repartimiento system, it did not help much is reducing Native suffering. It was only their replacement by African slaves that overturned this, but this did nothing to change the economies or social hierarchies that the colonies relied on.

The slow population growth of French settlements was caused by very different factors. For one thing, French colonization was not an act of military conquest and religious conversion, but rather the setting-up of trading posts for the extraction of luxury goods back to Europe. The French Crown wanted to make money on a cheap investment in effect, and not hold a massive empire as the Spanish did. No more than 5000 Frenchmen (and they were almost always men) came to New France between 1602 and 1672, and the largest contingent of them would have been coureurs-des-bois or otherwise involved in the fur trade. Seigneuries, another post-feudal system, became common along the St-Lawrence by the early-to-mid 1700s, and by the beginning of Seven Years War it can be certainly be said that the colony had moved beyond simple trading posts, but they never grew so big as to be able to push their weight around. They preferred diplomacy and alliance with the natives.

Another factor is that France did not allow protestants into New France. This meant that they did not have religious minorities constantly coming over to escape the king's tyranny. This was a trend that contributed greatly to the population growth of the Thirteen Colonies.

Id like to take a moment here to say that I don't know all that much about settlement and French colonies in the Caribbean, other than it being slave economies and cash crops. I will let others speak about this if they would like.

And so at last, let's talk about English/British colonization, and why it saw rapid population growth where France and Spain did not.

The first English colonies in the Americas were business ventures set up by joint stock companies, the Plymouth Company and the London Company. Population growth was initially quite slow, but once cash crops like tobacco were discovered, settlements such as Jamestown began to prosper. Moreover, the English crown was not afraid to grant charters to religious minorities as mentioned earlier, even granting one to a Catholic Baron which did not include religious restrictions. Ever since, Maryland has been the "catholic state". Another example is the Massachusetts Bay Colony, set up by puritan separatists to distance themselves from the Church of England. Such things would not have been allowed under the Spanish or French systems. So as you can see, the English were already using their colonies not just for economic exploitation, but as a way to deal with certain demographics.

But even with more people settling, the rapid growth of the colonies would see in the 17th and 18th centuries was attributed mostly to a high birthrate, low deathrate, and large tracts of sparsely populated land that could be settled. The economies relied on slavery in many areas which, as we saw before, is a discouraging factor for large-scale settlement. But other areas were very short on labour and full of opportunity for those who came over.

Anyway, I hope that at least partly covers your question. There are likely other factors, but the points stated are certainly important factors in why Spanish and French colonization was slower, and British colonization was faster.

This is not to refute the premise of OP or other answers here, but I wanted to address the idea that the British colonies in North America were being "filled with settlers" in the sense that they were filled with people immigrating to the colonies. Immigration was important, clearly, but it wasn't waves of millions.

First a word on the population history of British North America (and as a sidenote, I'm specifically dealing with its white and black inhabitants). The population of the region today is pretty massive, and even by 1776 it was large and growing fast (it was 2.2 million in 1770, 2.8 million in 1780, and 3.9 million by 1790, and that's even with a war and substantial emigration of Loyalists). But we need to place that in perspective that these numbers came from a really low base that stayed quite low for a long time. The English colonies didn't break 100,000 in total population until the 1670s. It didn't break 1 million until 1750 or so.

Much of the immigration that did happen wasn't even substantial relative to the times. For instance, the Puritan Great Migration to the New England colonies in the 1630s is estimated to have been some 30,000 people or so (many of whom returned to England during the Civil War and Cromwell era). It's actually estimated that more Puritans immigrated to the Caribbean island of Barbados than to New England, and substantial numbers of Puritans also immigrated to places like Ireland as well. While we're on the topic, the population of New England was probably lower in 1700 than it was in 1600, when there were no European immigrants or their African slaves, and the native populations had not yet suffered from war, displacement and disease.

Anyway, it's hard to get precise numbers for the amount of European immigration to the 13 colonies before American independence, as the only real consistent annual records of such information are those kept by Philadelphia in the mid 18th century. Modern estimates generally put European immigration to the 13 colonies in the range of 310,000 for the 18th century (compared to about 280,000 imported black slaves), although individual estimates have tended higher and lower. I'll also throw in that a not-insubstantial part of that white immigration was itself involuntary in the form of convicts - Georgia was originally founded as a convict colony, for example, and there are estimates that these transported convicts totaled some 50,000. Even in the 18th century these immigration flows weren't consistent over the entire century: they were extremely low in the early decades and really began to pick up around 1730.

So what gives with the high rate of population growth in the 13 colonies? It was mostly because of natural increase, ie the white and black populations had extremely high fertility rates, and relatively low mortality rates.

Anyway, I just wanted to provide that background. It absolutely doesn't negate the question because, for example, clearly far more people were immigrating to the 13 colonies than to Quebec or what is now Canada. But we should be clear that North America as a destination for huge numbers of immigrants is really more a product of the period after 1820 than before (even in the first years of the United States, immigration was fairly low).

ETA just to give some comparative numbers for French North America - the "founding population" of immigrants to Quebec is often given as 10,000, but the Canadian Museum of History notes that broader definitions including people like temporary immigrants can put the totals closer to 20,000 - 30,000. Another 7,000 are estimated to have immigrated to the Maritimes, as well as 7,000 Europeans and 7,000 Africans to Louisiana. So not insubstantial (and remember this is only to 1763), but immigration to the 13 colonies to 1776 is probably about ten times that.

ETA 2 I don't really see good numbers for Spanish immigration to the Americas in the colonial period, and it would really be hard to make a decent comparison anyway since we are talking about three and a half centuries, so a period twice as long as the English colonial period in the 13 colonies. Estimates I'm seeing are in the low hundreds of thousands for the 16th century. But one thing historians of Spanish immigration are clear on is that more people emigrated to the Americas from Spain in the period of 1880-1930 (some four million) than in the previous four centuries combined. And I think that again goes back to a point that no matter how you cut it, mass European immigration is really more of a phenomenon of the 19th century onwards than the 16th-18th centuries.

The problem was not at all that individual Spaniards and Frenchmen were reluctant to immigrate. After French and Spanish (and Portuguese) colonies split from their respective overlords, immigration very quickly flourished, especially from Spain. So at a glance you'd think that immigration had been limited before that - and you would be correct.

Spain and France both pursued different strategies in their colonization of the Americas than Britain, and had laws directed towards this end. One could not simply up and leave France/Spain and go live in their American colonies, you needed to first have a certain status and an actual purpose that the authorities deemed useful - so usually nobles moving over to manage/establish land holdings or administrate, or professionals who would support the everyday running of these colonies, or at least mercenaries with a proposal for a new colonial conquest.

The French colonial presence was, in simple terms, based around securing privileged access to New World trade goods. Their settler presence was directed towards this end: to secure themselves a foothold from which they could trade with Native Americans. This didn't require a lot of settlement at all, so at their height they had at most around 100,000 settlers in North America. In disputes with other European powers, they relied very heavily on alliances with Native Americans, who would often choose to side with the French over Britain especially because the French, despite claiming frankly ridiculous amounts of territory, weren't very interested in actually settling it, while the British were constantly trying to actively seize Indigenous land.

The Spanish, on the other hand, entered North America with the same intentions that they had in South and Central America: to subjugate native populations, rule over them, and use their labour to derive economic benefits for the metropole with the bare minimum presence of Spaniards needed to achieve this goal.

This worked out for them in Central and South America, where they faced a lot of sedentary farming populations who in many cases were already parts of an imperial political structure. So they were able to insert themselves into pre-existing political structures as the new boss, so to speak.

In North America this simply didn't work out for them. North American native populations, while not necessarily 'nomadic' nor 'hunter gatherers' as most of them were skilled agriculturalists, were less tied down to specific tracts of land and in most cases were independent polities without established hierarchical structures between them. On top of that, by the time meaningful colonization of North America had begun, escaped horses from Mexico had long since headed north, and native populations in North America had already learned to use them to great effect, taking away one of the Europeans' most important advantages in warfare up until that point. There is also a different hypothesis that a different breed of horse was native to North America, and so North American natives had been using cavalry for much longer than my first claim might suggest. Either way, they had horses and they knew how to use them in combat.

So those factors made it impossible for the Spanish to gain a foothold in North America in the same way they had from Mexico and southwards. They had relatively little leverage in North America in comparison, as North American natives were both their equals in combat and lacked the more exploitable hiearchical political structures that were common to the south. They had no exploitative emperors who they might want to ally with the Spanish to bring down, no massive civil wars, etc. They simply offered very little to North American indigenous peoples politically. It was simply never sufficiently profitable for them to launch the large-scale military expeditions that would have been required to conquer them, and even if they somehow had managed it, their means of colonial exploitation wouldn't have worked very well there at all. Keep in mind that Spain's initial foothold in Peru and Mexico had been gained basically by complete chance, when private expeditions succeeded beyond anyone's wildest expectations. That was not something that was very prone to easy replication and especially not with the totally different circumstances in North America.

Britain on the other hand had more of a tendency to exploit their colonies through the encouragement of the direct settlement of British subjects. They would derive benefits from them by monopolizing trade with them, taxing them, etc, while the settlers, through their strength in numbers, would be more able to impose their will on native populations and other European powers. This ended with British North America being immeasurably more populated than the Spanish and French territories, and from about 1700 onwards they started to outnumber even the Indigenous population.

It also resulted in a far more complete Indigenous genocide, as the British considered natives to be basically useless for them and nothing more than barriers to settlement. In contrast, the French had incentives to keep them around as they wanted to trade with them, and the Spanish, while engaging in plenty of genocide themselves, at least had some incentive to keep Indigenous people alive, since they needed them for labour.