The factories all calculate the GVWR based on the weakest link as the truck is configured at the factory. This includes the leaf springs that are installed. The AAM axles and wheel bearings used on GM/Chevy 3500 trucks is rated at 10,900 lbs. by the manufacturer.
My 2011 Chevy truck has the same frame and suspension and the rear weight when new was 2860 lbs. with the front at 4380 lbs. and a total truck weight of 7240 lbs. before I did any modifications. The front with the engine weighs a lot more than the bed as one would expect. Conversely when I have put a 3400 lb. load in the bed it added only 100 lbs. to the load on the front of the truck.
Usually a crew cab adds 200 lbs. of weight and it is split between the front and rear wheels. However, the extra passenger seats results in a 150 lb. per seat reduction in the factory payload rating.
I know many people who tow 5th wheel trailers with 2500 pickups and with zero problems. I see this on the highways as well and during trips I keep a tally of how many trucks I see towing 5th wheel trailers have SRW or DRW trucks and it is always 4 to 1 with more than 80% of the trucks having SRW. No surprise if you do the math.
Take two wheels with tires rated at 3750@80 PSI and you have a potential to carry a 7500 load minus the 3,000 lbs. for the truck or 4500 lbs. and if the truck is going to support 25% of the 5th wheels wet weight that translates into a trailer weighing up to 18,000 lbs. which covers 100% of the travel trailers.
People in the cab do not add significantly to the load on the rear axle and that is all you need to worry about. Take your truck to a CAT scale and get the weights at the front and rear wheels measured. Then add 400 lbs. to the rear of the crew cab and go back to the CAT scale and get the truck weighed again. Then you will know your situation exactly.
I replaced my factory supplied tires that were rated at 3195@80 PSI with ones rated at 3750 lb. and gained 1100 lbs. of payload at the rear wheels. Total cost for the change out was under $500. I spent another $445 for a set of SuperSprings to increase the load that the truck could handle up to 5,000 lbs. which was more than enough.
Air bags are an option but I prefer using the SuperSprings as there is nothing to adjust and nothing to break. If I were to lose only one of the two air bags on a trip it would be a serious problem.