Not sure about the specs on your F250, one of my trucks is a 93 F350 4x4 crewcab single wheel with a 9200 GVWR. The truck empty weighs 6260lbs that leaves 2940lbs for passengers & bed payload. We have a Lance 10' 9" camper that I have put on it a few times that weighs approximately 3200lbs loaded with gear & liquid. With two of us passengers & full tanks of fuel we are probably about 300 lbs at least over weight for the GVWR. The truck handles the load no problem 70 mph on hills & stops in a resonable distance safely. This is still an unsafe ultimate condition over the GVWR, sure the axles are rated a bit above this for engineering safety margine. I hadn't towed with the camper on & would imagine that if I did things might be a bit different for braking distance.
Adding air bags will not increase the GVWR, it will shift your load forward to more evenly distribute the load for better handling.
What has happened in our case, out of the blue my company is now paying a car allowance which has afforded the purchase of a new F350 PSD CC DRW 4x4 with a 13,000 GVWR which is more than enough to haul the camper & tow 10,000 lbs plus safely without taxing the driveline as well.
It's really up to the individual how much you want to tax your driveline longevity & safety

My 2 cents.....