Why did each of the states write a constitution as soon as independence was declared

Congress asked the 13 original colonies to form governments for themselves, so the colonies began writing and adopting new constitutions to become sovereign and independent states.  . However, the national government was weak and states functioned like independent countries. So, at the 1787 Constitutional Convention, delegates from the different states decided to a plan a stronger federal government with three branches (executive, legislative and judicial) all of equal power. As a result, the US Constitution was signed on September 17, 1787 in Philadelphia.