In California, as nearly as I can tell from reading the V.C., it is illegal to load a truck more than the GVWR, but the violation is one of tax and registration codes, not safety. I other words if you are running 11,500 in a truck registered at 11,000 lbs, you didn't pay enough registration. Exceeding tire ratings I think is a safety code violation. I cannot find anything similar for GAWR except perhaps for heavy commercial trucks (and this relates more to axle loads and their effect on paving).
There are provisions for the judgement of the patrolman - if he thinks you are overloaded, then you may be overloaded.