Final answer:
The weaker political party between 1788 and 1800 was the Democratic-Republicans, who were initially overshadowed by the dominant Federalists but gained power after the Election of 1800, leading to the Federalist Party's decline.
Step-by-step explanation:
Between 1788 and 1800, the weaker party in American politics was the Democratic-Republicans. The Federalist Party, with leaders like Washington, Hamilton, and Adams, dominated the political scene in the 1790s. However, the Election of 1800, often referred to as the 'Revolution of 1800', marked a turning point as Thomas Jefferson and the Democratic-Republicans gained power, leading to the gradual decline of the Federalist Party.
Despite their initial weakness, the Democratic-Republicans managed to attract a wide range of supporters, from wealthy landowners to new immigrants with radical ideas, and were strong in the South and parts of the North. This shift in power was significant in the development of the first party system in the United States and played a role in shaping the government's response to events like the French Revolution and the Whiskey Rebellion. The Federalist Party's decline was hastened by opposition to the War of 1812 and the Hartford Convention, eventually leading to the Era of Good Feelings and one-party rule under the Democratic-Republicans.