For standard truck rims the highest load capacity tires provide 3750@80 PSI or 7500 lbs of load capacity at the rear axle. Two options to increase this with the easiest being to go to a DRW pickup and have 4 tires at the rear axle. An alternative to consider is spending $3000 for a full set of four 19.5 wheels and tires as these have a load capacity of 4800 lbs each or more.
If I had to choose between 19.5 wheels and tires and a DRW truck I would go with the 19.5's in a heartbeat. A DRW is a pain to park and the 6 tires do not fit in a rotation pattern and having to change an inner tire on a pickup with a heavy camper sitting in the bed is not something I would want to face.
But it is entirely subjective and most people go with DRW as it is a simple decision. The same subject comes up with 5th wheel travel trailers and yet I know people who have no problems with their 13,500 trailers being towed with SRW trucks. When traveling I will keep a count of 5th wheel RVs that pass us on the highway and consistently more than 80% are towed by pickups with SRW.