Just so you know, the DOT in ANY state can pull you over for pulling a trailer, empty or loaded. They DO NOT need a reason. They can actually pull you over if you are driving down the road with a stepladder in the back.
It's all part of the Federal Safety Regs., I'm not saying it's right, but they do have that power.
What you should have done is stopped at the closest CAT scale and weighed your rig before leaving out.
In the future when you leave out from anywhere, stop and weigh it before you get pulled, CAT will go to court with you and help defend you in the case if you should get pulled over again for that. It costs 10 bucks, but it's good security.
Again, I'm not defending them by any stretch, I have to deal with them on a daily basis when I'm out in my big truck.
Unless your vehicle is registered to a business and you operate commercially I would seriously look into the log book violation. Also IF you are registered as a business you must have a chauffeurs liscense to drive that vehicle legally.