It starts with the French Indian War/Seven years war, England and a host of allies fought against France and it's allies. The majority of the land west of the Mississippi at this time belonged to France, as well as the areas in Ontario and Quebec.

France lost this war and the treaty of Paris was signed in 1763. This treaty signed over most of the Canadian territory to the British as well as areas in the Ohio river valley, but, the lands west of the Mississippi went to Spain in a secret treaty signed in 1762 called the Treaty of Fontainebleau. This treaty effectively gave control of that territory to Spain, so when the British wanted it the following year, the French denied possessing it so by right, they could not give it up.

Fast forward a few years and you'll get the American revolution fought primarily because of the over taxation of the American colonists for the French Indian War. The continental army under Richard Montgomery invaded Quebec in 1775, though they were able to capture Montreal, the subsequent battle at Quebec city turned disastrous and the Continental army was defeated. This marked the end of the Continental Armies invasion of Canada.

Now eventually the war was won by the Americans with the help of the French, however France in the Treaty of Paris in 1783 wanted to keep America isolated east of the Appalachian mountains in an effort to appease Spain who also entered the war to regain lost territory it had give up to England after the seven years war. Realizing this, the Americans treated with London directly and were able to gain a better deal granting them all lands east of the Mississippi, south of Canada, and parts of Florida.

The only problem with all of this was the fact that England pretty much abandoned all of its native American allies that helped fight against the Continental army. Once the 13 colonies were established, these intermittent American Indian Wars continued for the next almost 100 years with America winning the majority of them save for the Seminole Wars fought in Florida.

Since England still held Canada, American frontiersman began to settle west until the Mississippi which was the borders agreed to in their treaty with England, and all the land west of the Mississippi was still held on loan by the Spanish for the French. These borders pretty much continued this way until 1803 with the Louisiana purchase.

Napoleon wanted to build up the French colonial Empire it had lost in the Seven years war, and according to the Treaty of Fontainebleau, reclaimed all territory given to Spain in 1762. However major problems arose for Napoleon in trying to hold Spain itself as well as the colonies it had gained in his conquest of Spain. Holding this large territory west of the Mississippi river was proving to be too costly for Napoleon and his ambition to conquer North America were just to alien at this time for it to ever come to a reality. So as the story goes, the Louisanna purchase was agreed to between Jefferson and the French Empire.

During all this time Canada was split into two governmental bodies, upper and lower Canada, these two joined together to form one Government in 1840. It wasn't until 1867 that they joined together along with other territories in Nova Scotia and New Brunswick to form the country we call Canada today. - Edit thanks u/Zomunieo!

In the War of 1812, America and England fought each other with virtually no territory gains for either side. This war ended with the treaty of Ghent in 1814, allowing immigration for Americans moving westward and northward. This rush of immigration from America as well as England and Ireland led to roughly 80% of Canada being made up of English speakers which worried much of the Quebec leadership who rushed to gain control of territories to the west of Toronto. However it was basically granting immigrants more lands to colonize and from 1812, the population of Canada was around half a million and for the next 50 years, Canada's population would be boosted to about 3 times that number. So to answer your question, the whole idea of Manifest destiny which was mostly seen as being straight westward to California also lead to Americans immigrating to Canada. However most of the population of Canada at this time was made up of Scots, Irish, and British immigrants.

They tried to! Americans moved north in the War of 1812 with an unsuccessful invasion of Canada. They tried again to move north around the time of the Polk presidency - Polk rather famously campaigned on "54 40 or fight" (i.e. 54 degrees, 40 minutes as the border with British Canada) but negotiated a settlement at the 49th parallel, else much of British Columbia would be a part of the U.S. today.

But I would argue that there are a couple practical reasons. First, go back in time to the search for the Northwest Passage. What matters to folks is a sea passage, because sea transit is critical, and you'll see that in settlement patterns: the eastern seaboard and Great Lakes are first settled because that's the easiest way to move people. As a consequence, the eastern seaboard of Canada into the Great Lakes was already pretty well populated by, say, the war of 1812, and had been for some time, so that avenue was closed. If Canada couldn't be purchased a la the Louisiana territory, then it had to be acquired elsewhere, and there wasn't a particularly strong appetite for war (though incidentally there were murmurings of taking all Canada into the late 19th Century, but never much more than murmurings to my knowledge.) French Canada was never really going to be receptive to joining the U.S. Farther west of the Great Lakes, you get out of the Mississippi River delta and lose access to the coasts and major cities, so these areas would never be the first to be settled.

And that reason - geography, basically, and climate - is why California and Oregon were settled before much of the land that was taken in the Mexican/American War, or Texas, or most of the land in between, and why it remains much more densely populated there today - compare Oregon to, say, Wyoming, and ask why the U.S. didn't try to acquire a lot more Wyomings.

Frederick Jackson Turner wrote the Frontier Thesis in 1893, he noted that the frontier was closed. This was within memory of the Civil War, and just over twenty years after the opening of the Transcontinental Railroad. If you look at population density at the time, there is none with the great expanse of Canada and none in the U.S. states bordering those stretches of Canada. There was no populated border with Americans on one side and no Canadians on the other side.

For more I'd highly recommend Bruce Cummings' Dominion from Sea to Sea, which goes into the settlement of the West in great detail.