Did hamilton help write the constitution or was he just a devout believer in it?

You got it right. Hamilton was not a strong supporter of the Constitution. He thought we should have a much stronger central government. When the delegates were discussing the office of president he gave a long oration on the benefits of having a king. No one even commented after he finished. He got mad, left the convention and never returned. However, while he didn't return to the convention he became instrumental in it's page by the states by him being the author of most of the Federalists papers.