Why would early americans want a weak national government and strong states

First of all, the states did not originally intend to create one nation as is apparent when they called themselves a "league of friendship". By having a weak national government they could remain separate states while maintaining good relations with each other and the rest of the world.

Some form of central government was also necessary to win the war, but that did not mean it needed to be a strong one that could turn around and abuse the powers it was given.  

A weak government cannot abuse powers not given, and thus there would be no repeat of the colonist's experience with British rule. Also the colonists feared that some states would dominate in a national government and majority tyranny would result through representation, expenses, and territorial claims.