Why would the act of nullification have weakened the union?

Nullification is where a state has a right to disagree with a federal law they think is unconstitutional and not correct, and no longer abide by it. Nullification would have weakened the Union because states would no longer have to agree or act on certain laws, causing obvious conflict within the state and conflict between Congress and the state. The state would no longer be unified and a quarrel between people in the state, the states, and between the state and the Congress would deepen and would most likely lead to war and weaken the Union.