Two parts limit the payload, the tires and the leaf springs. If the sidewall on the rear tire states a max load of 3200@80 PSI then the total load is 6400 lbs. minus the 3000-3300 lb. weight of the truck.
It the tires can take the load then the next aspect is the leaf springs.
Once the camper is in the bed you can see if the truck sags in the rear. The odds are high that it will sag and so you add more springs using a $450 set of SuperSprings.
These trucks are designed to tow over 13,000 lbs. and the rear axles and wheel bearings are rated anywhere from 8900 to 10,900 lbs. so the load limiting factors are the rims/tires and the leaf springs.
Budget $800 for new tires, $400 for new shocks, and $450 for Supersprings, and possibly another $500 for a heavy duty anti-sway bar. These are common modifications required on most trucks to handle a 3,000 lb. or heavier camper load.