The notion that the US wanted to expand as much as possible isn’t really true. The US from the early 19th century until the Civil War was really not a single, united nation, but rather two competing sections. The Northern section veered away from an agricultural economy and more toward a commercial and industrial one. The southern section preserved a slavery-based agricultural economy up until the Civil War. Both sections vied for control of the Federal government, but (with some exceptions) the southern section controlled policy to a large measure in antebellum America.
Being an agricultural economy, the south certainly was interested in expansion. However, it wasn’t interested in just any territory. By the terms of the Compromise of 1820, any new territory north of the compromise line (set at the southern border of Missouri) would be free territory; any territory south of this line was slave territory. For practical purposes, this simply reflected geographical reality — territory north of the line is not well suited to plantation agricultural and cotton cultivation, but the south certainly did not want to add territory north of this line. Such territory would eventually form free states that would undermine the south’s influence in Washington. It looked to add territory south of that line, though, which would eventually form slave states perpetuating the south’s power.
That’s the reason for settlement of Texas by southerners, which eventually led to war with Mexico. It’s also a reason for lack of interest in Canada after 1812. Canada was in no way suited to slave-based cotton growing.