My understanding is, years ago only DMV cars/officers pulled commercial vehicles and got out the scales etc for random roadside inspections. But, they merged the departments into one, and ALL SHP officers are also DMV enforcement. I remember in the 90's seeing different DMV marked patrol cars. Those are long gone.
However, the chances a local cop or police officer is ever gonna pull you for a tag weight issue is gotta be single digits.
Also, for all those guys pulling 10 ton goose necks etc, be very careful pulling with your 1 ton truck, many have GVWR over 10k lbs, and its very easy to have a CGVWR over 26k, regardless of actual total roadside weight a class A is needed!