Well, I think you're kind of underestimating the Benelux countries' resources and advantages. Traditionally, from the Middle Ages onwards, the area has been one of the wealthiest and densely populated/urbanised areas of Europe. It's extremely well positioned to serve as the northern trade hub for Western Europe and has always had a fairly high agricultural productivity rate (thanks to the very fertile soil but there's also a fair few technological advances that originate from the region - something that was necessary to deal with the relatively sparse land in combination with the dense population). After the industrial revolution, mainly Belgium also had a very large supply of coal - crucial to industrialising.

That said, for quite some time, the regions were part of greater empires. It's not really interesting to talk about the pre-Burgundy Low Countries in response to your question, because the area was just a collection of smaller duchies and principalities and cities. But the first time the area was somewhat united, was under Burgundian rule - the dukes of Burgundy of course coming from the province in France and set on rebuilding the Middle Kingdom. After their line died out with Charles the Bold, the area came into possession of the Habsburg dynasty and eventually became part of the larger Habsburg and then Spanish empire. It's at this point, 1568, that the northern Netherlands - the modern Netherlands - revolted against the Spanish crown and (generally) remained independent. For Luxembourg and Belgium, however, this would only happen in 1815 and 1830 respectively. The point here being that for quite some time, the area didn't manage to stay independent. It's worth noting, for instance, that during the Dutch revolt, the area now known as Belgium also revolted against Spanish rule - it's just that this area was unable to escape the Spaniards. Arguably, the domination by larger empires could be seen as the reason why the area wasn't slowly picked apart and absorbed into the French or German sphere.

Now, as to the question post-independence. For the Netherlands, your caricaturisation as it being a small and weak country is somewhat mistaken. The Dutch came out of the Eighty Years War as a fairly strong nation. It was still one of the richest parts of Europe, it built a powerful navy and had a competent army. While you may look at the modern Netherlands being dwarfed by France, Germany and the UK, back then, this wasn't the case. Germany didn't exist - it was a collection of smaller states. While nominally united under the Holy Roman Empire, at this point the HRE was more an effort in herding cats than in unity. Having literally just come out of the Thirty Years War, being divided along religious lines but also just never really being united before, the HRE wasn't going to be the Netherlands' main concern.

Similarly, France had been involved in massive internal religious wars itself, but even when it bounced back under Louis XIV, the Dutch were never its main concern. While it fought, for instance, the Franco-Dutch War with the Netherlands, France was more interested in gaining territory from the then decaying Spanish Empire than from the Dutch. More of a threat to the Dutch were the English - while they certainly weren't even half the power they would eventually become, the English were probably the main competitors to the Dutch, leading to four Anglo-Dutch wars. Now, again, you can't look at the Dutch as a tiny nation at this point - it could go toe to toe with the English. The Dutch lost the first war, won the second and third (including the Raid on the Medway where the English suffered one of their greatest military defeats) and finally lost the fourth. Now, these wars weren't about survival, so to speak. The Dutch weren't going to conquer England (though with the Glorious Revolution, they kinda sorta did), the English weren't going to conquer the Netherlands. These wars were about naval and trade dominance. Winning the second and third war, the Dutch were the strongest trade and naval nation in Europe during the 17th century. Losing the fourth, that title went to the English. But this all goes to show that the Dutch weren't pushovers among giants.

A good note by /u/NFB42

I really disagree with this lining up of the four Anglo-Dutch wars. The first three took place within 20 years of each other. The fourth took place over a century later. The Anglo-Dutch conflict ended decisively with the Glorious Revolution, the subsequent events perhaps best described as the Dutch winning the conflict, and the English winning the peace. By the time the fourth was fought England had already eclipsed the Republic, and presenting it as a continuation of the 17th century conflict just misrepresents both, imo.

I'm getting off point and I've already typed too many words, so I'll make the rest a bit more abstract. Post-French Revolution, things became more like you described them in the OP - while the Low Country countries didn't get weaker, quite the opposite, they were rapidly outpaced by a booming France, Prussia and then later Germany, as well as Britain. But this ended up playing into the hands of the smaller nations in terms of territorial integrity. I've written about some creation myths about Belgium before - about the claim that Belgium was created by England as a buffer for France. The reality is that England intervened diplomatically to prevent Belgium from falling into the Francosphere - this illustrates a greater point that resentment between great powers, efforts of these great powers to protect the countries in their sphere, and so on helped the smaller countries survive. The same was true for Luxembourg which served as a Prussian buffer against France.

The last thing I want to do is to present these countries as surviving at the whims of the bigger boys, however. A good example of how the smaller countries used competition between the larger nations is, of course, Congo. At the 1884-5 Berlin Conference, Leopold II of Belgium managed to pull of something of a diplomatic coup by coming out of it with Congo as his private property, an area almost 80 times larger than Belgium itself. (note that this isn't how the Netherlands and Portugal got its colonies) The Benelux countries also had to actively manoeuvre themselves on the diplomatic front to protect themselves - by declaring themselves neutral, for instance, an important cornerstone for both Belgium and the Netherlands during the 19th and early 20th century.

It also helped that during the 19th century, the attention of the parties traditionally interested in the Benelux were focussed not only on each other, but also outside of Europe. So not only would attacking one of these countries bring along several other large countries into your dispute, it was also much easier and more profitable to focus on colonies and so on. The cost-benefit analysis for invading these countries just didn't really make it an attractive prospect. A good example of this in the 20th century is the first World War. Germany invaded Belgium to get to France, the benefit outweighed the cost, but left the Netherlands alone - despite it being in the Schlieffen plan - because Germany thought that it got the benefit of getting to France by going through Belgium already, thus they saw invading the Netherlands as a cost-only operation. (massively simplified, I know) Also, if you look at wars during the 19th century, they weren't the same as they were pre-French Revolution. They were mainly colonial and trade disputes (fought in the colonies and on the seas), wars of unification (which these countries wouldn't be part of) and wars generally revolving around dominance (Franco-German war). Generally speaking, this left the Benelux countries uninvolved.

Of course, there's more to independence than just military might. Economically speaking, for instance, both the Netherlands and Belgium did very well and were punching way above their weight - in no small part because of their colonies. The Netherlands always remained a force to be reckoned with in global trade, while Belgium was the second country to massively industrialise. This made it harder for the larger countries to economically bully these countries.

God, I keep making these posts and I always forget to prepare a general point from the get-go, so I just ramble on and add things as they spring into my head, with the whole thing fizzing out near the end. I guess a tl;dr could be: Countries like the Benelux certainly weren't always independent and arguably, this kept them out of the hands of the German and French spheres. When they did become independent, they often relied on bigger powers being too preoccupied with each other to focus on them and actively played into this situation to get themselves ahead. And regardless of their size, certainly the Netherlands and Belgium became countries to be reckoned with in fields aside from military might and population numbers, guaranteeing their independence. The biggest factor was that due to diplomatic and economical concerns, they were never really attractive targets - there was always someone better out there to invade.

So there. That's an answer. It's certainly not complete, but it may serve as a short (?) introduction.