I found there were four primary categories into which territorial acquisitions fell:
1. Purchase, land that was sold to the US that wasn't part of a peace treaty. I added the peace treaty caveat because technically the US compensated Mexico for the territories it gained after the Mexican-American war, but Mexico would have never sold that land had there not been a war.
2. War, land gained as a result of a peace treaty.
3. Annexation, land gained through unilateral action, such as unchallenged land claims or when a local independent government chose to join the US.
4. Treaty, unclaimed land that was peacefully gained based on an international treaty.
These percentages are, of course, estimates as treaties generally didn't specify the size of the territory being claimed, and often borders were disputed and changed. They also only include territory which the US currently holds, so the Philippines and several other Pacific territories are not included.
While half the US wasn't purchased, purchased territory makes a plurality of the US. The single largest purchase was the Louisiana Purchase (22%), followed by Alaska (17%).
The single largest transfer of land was the Revolutionary War (24%), which means the US has quadrupled in size since independence.
As for annexations, most of that 11% is from the annexation of Texas (10%). While the Oregon Treaty (8%) which gave the US the Pacific Northwest makes up most the treaty category.
Texas was actually hard to categorize as, while it was annexed prior to the Mexican-American War, that annexation certainly led to the Mexican-American War. If one were to include Texas as gained through war, the Mexican-American War would rival the Revolutionary War as the single largest transfer of land.