I am a single mother of a 3 year old. I would like to move to another state, I currently live in Michigan. I have an order for child support but receive none. At this current time his father takes him Friday and Saturday. But I would like to move?

You have to get the father to agree.

Even if I have full custody? I chose to let him see him on the weekends

Even if I have full custody? I chose to let him see him on the weekends

Right now you choose. If he disapproves of the move and since he has been visiting the child the courts will choose for you. And more then likely they will grant him more then he has now.
Bottom line is if you want to move seek the courts approval as well as the dads.

If there is no court ordered visitation, you MIGHT get away with it. But would you like to move and have a court order you back? Get approval first.

Full custody does not mean he does not have a RIGHT to visits, so if he does not have a visitation order and you move, he may file right away for one and a order to make you move back, and if you don't move back, he could even get a order giving him custody.

So it would be best to get his permission