People didn’t much like the front runner Dem Mark Green. Then 9/11 happened and Guiliani endorsed Bloomberg late in the game. Bloomberg at that time was running as a Republican.
He didn’t have to be sensitive about his height in NYC - he was one of many short Jews and Italians. Different when you run for president.
Puerto Rican and Peruvian New Yorkers make the Jews and Italians look like basketball players