First of all, we weren't the only ones who claimed the land. The Spaniards and then the Mexicans were in the Southwest, with longtime settlements there. The British were in Canada, with designs to keep claims on the Oregon Country, so as we moved westward as a nation, this put us into political and sometimes military conflict with other nations and empires.
Also, because of the move west, we added a lot of agricultural territory, some of which became cotton producing and which had legal slavery. Britain needed to cotton for its factories, but would rather we did not have slavery. When the Civil War came around, they would be torn as to whether or not they should enter the war on the Southern side.
John O'Sullivan a New York journalist coined the phrase "Manifest Destiny". His article suggested that it was a "divine mission' that the U.S. would spread democracy from sea to shining sea. However, U.S. westward expansion was entangled with the policies of foreign nations. The U.S. domestic agenda was propagated on how well it dealt with its foreign relationships. The following were to the benefit of the U.S.
1. 1803 Louisana Purchase- from France
2. 1818 Northern Border- at the 49th parallel in exchange for the Great Lakes w/ Great Britain
3. 1819 Flordia- Adams Oris Treaty/ acquired Texas at the 42th parallel w/Spain
4. 1842 Webster-Ashburton Treaty w/ Great Britain
5. 1845- Independent since 1836 Congress agreed to Texas being annexed
6. 1846- U.S.treaty with Great Britain to extend the 49th parallel from the Rockies to the Pacific
1848- The Mexican Cessian- U.S. paid 15 million dollars for much of the southwest
1853- The Gadsden Purchase- to complete the Transcontinental Railroad.