There's a tire pressure sticker in the door jam and that pressure will support the truck's GVWR. Increasing tire pressure or fitting LT tires does firm up the sidewall and will increase the tire's weight capacity but does not change the the vehicle's weight ratings. Look at the weight capacity of the OEM tires and they're more than competent and greatly exceed the axle weight ratings.
You're getting close to GVWR with a 7800 pound trailer and at least 780 pounds (10% is the minimum for a conventional trailer) on the ball. Your tongue weight is?
Seems most folks run out of cargo capacity before they run out of towing capacity towing conventional trailers due to tongue weight. (Motor) Boat trailers put much less weight on the ball due to their geometry and aft weight placement.
-- Chuck
Those are good points. My tongue weight is 900lb, which is the limit for my Expy. I shifted weight around in the trailer to get it down to 900lb. My GVWR is 7720lbs and I'm at 7120lbs with the trailer in tow. My front axle is rated at 3550lbs and I'm at 3080lbs. My rear axle is rated at 4380lbs and I'm at 4040lbs. I've made many visits to the scale to make sure I'm in line with the numbers.
But all that said, it's still a lot of trailer for the Expy. I'm looking at getting a Super Duty or RAM HD. My travel trailer is 33' long, and that big of a sail with that much weight pushes the Expy around (no sway, just push from wind and semis). I have a ProPride hitch, Bilstein shocks, and LT tires. All of that helps, and it tows fine in ideal conditions. But I've pulled in 35mph crosswinds and it's not comfortable.