Looks like you have a similar truck to mine which is a 2011 F-350 SB 4X4 6.7L with 20" wheels. The rear GAWR is 7000 lb and the 20" Michelin tires (LT275/65R20/E 126 R) are rated at 3750 lbs each:
http://www.michelinman.com/tire-selector/name/ltx-a-t2-tires
When I went shopping for trucks, I was surprised at the low payload capacity of a 3/4 ton and so I went for the 1 ton.
Even still, I am only hauling a Northstar 850SC popup which has a dry weight of 1960 lbs. So if I add 350 lbs for water, 500 lbs of gear and 500 lbs of passengers and 120 lbs tongue weight for my boat I am very close to the advertised payload capacity of 3418 lbs.
The dry camper rear axle weight (no passengers or gear) was a modest 5300 lbs.