The odd thing is that technically any pickup truck in CA has to have commercial plates and pay the extra fees but with regard to commercial trucks if they are pickups you are never going to have to stop at a weigh station in this state - Utah is different in this regard.
CA gets you at the DMV and after that you are going to be left alone, especially if you are not engaged in anything that looks like a commercial enterprise. Someone pulling a very large livestock or horse trailer could expect more scrutiny but it is still highly unlikely.
The CHP that target trucks are looking for grossly overloaded vehicles that are unsafe or beating up the highways. Other than that they prefer to focus on catching speeders.