Why does the law varies from state to state?

There are certain areas that the laws are not laid out in the constitution or any of its amendments. If it is not addressed in any of the previous, it is under the jurisdiction of the individual states, counties, cities, etc. to define what is legal and what is not. This seems to work okay because in the constitution and amendments it specifically lays out areas which local governments cannot touch, leaving whatever is leftover to local areas. If there is widespread support for a change, further amendments can be made.