How did the United States benefit from its victory in the war of 1812?
It's hard to call that war a US victory, but it did force Britain to take American shipping and foreign policy seriously.
Canadians believe they won the War of 1812; America attacked Montreal for what they figured would be an easy victory against a British proxy. They didn't do it twice.
The British believed it was a minor theater of the Napoleonic wars, which they ultimately and decisively won.
American ships were being boarded regularly by the British navy, and American crew and passengers were forced into service on British ships. Also, American ports (notably New Orleans) were blockaded by British ships. These practices were ended by the war, which felt like an American victory.
The clear losers of the war were Bourbon Spain (which lost Florida) and the various Native American tribes that sided with the British. When General Jackson later became President Jackson, his payback to those tribes killed or removed nearly all of them to present-day Oklahoma. This is known as the Trail of Tears.