CHP can be a stickler, if they want to be. But for sure, you'd better not be over either of your axle weights, or the carrying capacity of your tires. Of course, to determine if you're overweight, they have to be able to weigh you, either with portable scales or at a scale location along the highway. Also, you have to have the proper 1)registration for your truck, 2)and for your trailer, 3)and your driver's license, and all of those can depend on the weights of your truck and trailer.
Personally, I would go to the CHP with your paperwork, weights of truck and trailer and ask them if they see any problems. Tell them you don't want to violate the laws, but they are complex and you get different answers depending on who you ask, so you need an expert. And you can ask how much more weight you would be allowed if purchasing a new trailer. The reason I say this is that at the local DMV offices, they don't understand the laws in the same way as do those enforcing the laws. And it's the people enforcing the laws that are the most important.
I had an experience with the KS registration people telling me one thing, but the law said something different. I sent the registration people a copy of the law from the Kansas Legislature website and pointed out what the law actually said. The gal said that she had been there for 24 years and they had never done it that way and that the law was wrong, but, just because I was being so nice to her, she would call SGT. X at the KHP and ask him. Well, she did, and SGT. X told her that what she had been doing for 24 years was wrong. So the moral of the story: go to the law enforcers, not the administrators in the offices.