Well, I realize that the Bird is a semi-genius, and has verified most of the facts in the Encyclopedia Britanica, and if he says that things registered as RV's or had an axle removed don't have to stop, and he hasn't seen it, it must be so! Randy is right about 1 thing, if you comply with the State DOT regulations in the States you operate in, you'll have no problems!
I found this summary from the AAA website, and since its on the web, it must be 100% accurate. I had a feeling this might be the case based on the 40 years I've had dealing with FAR's, FMCSR's and State DOT's, but the Bird is the official verifier!, ps, I personally got a ticket in Oregon pulling a very private dually and a small float with 2 golf carts on it! Oregon uses a weigh in motion, photo enforcement system, so your education will show up in the mail!
In 22 continental states, personal vehicles must stop at weigh stations if they are over a given gross vehicle weight rating or gross combined weight rating. The GVWR is the total weight of the vehicle loaded to capacity. The GCWR is the total weight of the towing vehicle loaded to capacity plus the total weight of the trailer loaded to capacity. The GVWR of a vehicle is the same wether the vehicle is loadejd or empty - it is the manufacturers's rating and it is almost always listed on a plaque or sticker on the vehicle or trailer. So even if the vehicle is empty, these requirements apply.
The following list may not be perfect, but it was the best I could determine using the info on AAA.
As best I can determine, it is rare that personal pick-ups or RVs pulling trailers are prosecuted for failing to stop at weigh stations, but I am posting the legal requirements even though they are rarely enforced.
In Arkansas, Georgia, Iowa, Indiana, Louisiana, Massachusetts, Minnesota, New York, Nevada, New Jersey, Ohio, Oregon, Rhode Island, and Wisconsin, all vehicles with a GVWR or GCWR over 10,000 lbs must stop at weigh stations.
In Michigan, all vehicles with a GVWR or GCWR of over 10,000 lbs with dual rear wheels must stop at weigh stations.
In Nebraska, all vehicles with a GVWR or GCWR over 10,000 lbs must stop at weigh stations except pick-ups pulling a camper trailer.
In North Dakota, all vehicles with a GVWR or GCWR over 10,000 lbs must stop at weigh stations, except RVs.
In Montana, South Dakota, and Wisconsin, all vehicles with a GVWR or GCWR of over 8,000 lbs must stop at weigh stations.
In Virginia, all vehicles with a GVWR or GCWR of over 7,500 lbs must stop at weigh stations.
In New Mexico, all vehicles with a GVWR or GCWR of over 26,000 lbs must stop at weigh stations.