as you see there is a lot of info on licensing that our state dots keep up with and doesn't pertain to non commercial vehicles. Your question is a weight question.
In OK the laws regarding the trucks GVWR/RAWR/FAWR/TIRE caps are the same when weighing for a overload condition either commercial or non commercial. GVWR is a bit different for a combined plate. My OHP troop L near me, shift captain says were just not interested in RV's UNLESS the tail is dragging or has a bad handling condition and all over the road. A OKDOT field officer told me the same thing as they may/can stop any vehicle on the road for weight check. He also said they weren't interested in RV's but repeated the same thing the OHP trooper said.
I towed my first commercial load, making a living, in '64 and have done so moore off than on since. More of a part time thing but I keep up with the latest OK state weight requirements/changes.
I have been stopped for a RV weight check by a OK trooper. Had a 9.5" truck camper on a '67 1500 chev. Luckily I was under the door tag RAWR. BUT I was over GVWR. He suggested I uprate my GVWR to = GAWRs when new tag time came. I did. No ticket issued as GAWR/tire cap is what we get weight for.
I live in rock crusher country and dot/troopers/county run constant road side rolling weight checks. The last time I went through with my 5er they asked if I would like a weight check. Yeah, they were training a couple of OHP troopers that were DOT certified for our new S troop (commercial division). I already knew I was under GAWR/tire caps . They had me pull up on the portable scales and got the GAWRs from the door tag. No probs.
I have paid a overweight ticket with a 3500 DRW truck with a bed full of wet crusher run gravel. The tickets was written for overweight axles. I was given a choise of unloading. It was cheaper to pay the 37.50 ticket. No shovel.
I also had a TXDOT officer in Lubbock,TX weigh me when I was hauling commercially with a cdl/dot number/etc. I was hauling motorized construction equipment and the yard had loaded to much on my trucks rear axle. About 1200 lbs worth. The TXDOT was nice and let me move more weight to the trailer so I would be under RAWR/tire caps.
As other posters say the fed mandate the states enforce 49 CFR regs pertaining to GAWR/tire caps/GVWR so each stae may vary on who they want to stop. Just 'cause some tow illegally and get by doesn't mean we have no weight laws regarding non commercial rigs (RVs).