When Congress passed a bill that added seats, in the House of Representatives, to Northern states, but not to Southern ones, Washington knew he had to stop it. But he did not want to seem like he was favoring the South over the North.
Thomas Jefferson wrote to him crying out against the voting which was nearly perfectly along geographical lines. However, Jefferson also came up with constitutional grounds for a veto. The Constitution only allowed for a certain number of delegates. The bill would have put Congress over that number.
Washington quickly used that as reasoning to veto the bill, and sent it back to Congress. Who instead of trying for a 2/3 majority vote, to overrule the President, took up another suggestion from Jefferson.
A new bill that would add delegates, but by using math. The new bill allowed each state a representative for every 35,000 citizens. Which while still just as unconstitutional as the first, was not controversial, as at the time population was pretty evenly balanced. And so the second bill passed.
Washington would only use one other veto throughout his eight years as President. His second veto went on a bill that sought to cut the number of cavalry units allowed to the federal government.