The animosity between Hamilton and Burr dates at least to the deadlocked election of 1800, in which both Thomas Jefferson and Burr received the same number of electoral votes for President (even though Burr was the Vice Presidential candidate). The deadlock was resolved by the House of Representatives, which chose Jefferson after 36 ballots.
Alexander Hamilton, a Federalist, opposed Jefferson and Burr, both of whom were Democratic-Republicans. But he feared Burr more, and worked to get Federalists in Congress to vote for Jefferson. In this fascinating letter to Harrison Gray Otis, Hamilton explains why.
Hamilton thought Burr (whose debts were legendary) would inevitably be corrupt because he lacked private wealth. Though Hamilton himself rose up from obscurity, he believed in a ruling elite with wealth and manners. Burr had a notable American lineage—his father was president of the College of New Jersey (Princeton) and his grandfather was the theologian Jonathan Edwards—but no money. He was an aristocrat but also probably far more democratic and far more of a politician as we now understand the term. Burr made no bones about using his office—whether it was his law firm, U.S. Senate, New York legislature, or Vice Presidency—for selfish purposes. He was not, at least, a hypocrite.
Indeed, Wood argued that Burr was “a traitor not to his country but to his class.” Burr was self-serving, routinely scheming to avoid bankruptcy. This was not how the founding fathers, who were supposed to be enlightened, nonpartisan, and disinterested landed gentry, were supposed to govern. Even Thomas Jefferson loathed Burr, as he tried to bend the Constitution in an attempt to convict his erstwhile VP of treason in 1807.