I think chains are the only requirement in every state. After that, it's all up the individual and their unique rig. Laws about WD would cause a total nightmare. Where and when does it begin and end? A 3500 towing a tear drop? or a pop-up camper? Um... you get the idea?
NO. Never heard of state requirement anywhere for weight distribution ... chains and length of rig, yes. Number of trailers that can be towed, and which type of trailer, yes. Which type of rig and special drivers license, yes. But never Weight Distribution.