Why did Federalist Alexander Hamilton back Thomas Jefferson over Aaron Burr after the election of 1800 reached the House of Representatives?

Hamilton believed that Burr would be more dangerous to the presidency

Explanation:

At the end of a long and bitter campaign, Jefferson and Burr each won 73 electoral votes, Adams won 65 electoral votes and Pinckney won 64 electoral votes. The Fedralist swept the new England, the democratic Republicans dominated the south. the democratic republicans failure to execute their plan to award Jefferson one more vote than Burr resulted in a tie. after all the election drama Hamilton personally favored Jefferson over Burr and he convinced several Fedralist to switch their support to Jefferson giving Jefferson a victory on the 36th ballot of the contingent elections.