Your max payload is ~1863lbs. Your GCWR is 11000 lbs. You mention that your GVWR is 6250 lbs. According to the link, your truck prolly weighs ~4387 Lbs
http://www.fordtrucks.com/specs/2003/2003_f150_1.html
If you had a camper in the back that weighed 1860lbs, You could tow a trailer that weighed ~4750lbs (11000 - 6250 ).
This doesn't take into account fuel, passengers, or gear.