First change out the rims for some 18" ones that will fit your truck. These will enable you to use a lot more tires rated up to 3800 lbs at 80 PSI with their 8" width. Lots of people get 1-ton GM trucks and decide to put on fancier wheels and so are selling their old wheels and tires for very little.
Second step is to add SuperSprings SSA-13 that will cost $450 and take 1 hour to install. These will improve the payload up to 5,000 lbs. so the weak link becomes the tires. Two 3750 rated tires provide 7500 lbs. of support and subtracting 3200 lbs for the weight of the truck on the rear tires that leaves 4300 lbs. for a camper.
Best to be conservative and look for a camper with a dry weight of no more than 2700 lbs. so when fully loaded for a trip the load is going to be less than 3500 lbs.
You may be able to find 16" tires with the load capacity you need but usually they require a 7.5" width rim.
For $1000 you can get the 18" set of wheels and tires and the SuperSprings. Then all you need are tie-downs and turnbuckles for the truck.
