My experience was about twenty years ago. I had a GMC 1.5 ton with a flatbed. It had comercial plates but they were for a pickup. Apparently the CHP called my license plate in and found it was licensed as a pickup. He gave me a citation for improper registration. To license for the flatbed, I had to weigh the truck. The officer did not weigh the truck but had scales and could have.
Personally, I have never seen or heard of the CHP weighing a RV of any kind. I had a 4200 lb TC on my '96 2500 SRW for over ten years, went halfway across the USA and Canada. Never questioned.