I have a 2011 F250 Lariat with the 6.7 diesel with Firestone airbags.
As others have said, the weak link are your tires. My stock Continentals were rated at about 3,000 lb load each, my new Michelins are load range 123 or about 3415 lbs. Both of my rear Continentals tires failed with less than 30,000 miles them towing a 12,000 thirty foot toy hauling trailer.
Basically F250's are made to handle 3000 lbs per tire, 6,000 per axle, 12,000 lbs total, minus the weight of the truck, gear, people, gas etc. that's the weight you can safely carry in the bed or on the hitch.
Air bags and weight distribution hitches don't increase your carrying capacities they just help level your truck.
You need a F350 dually to safely pull a 39 foot 5th wheel.