Yes, 4000 will likely be too heavy. Fill your truck with fuel, and go to a scale and weigh the rear of the vehicle. Subtract from 6800 (2 x 3400). That's going to be the tire capacity.
My guess is the rear is around 3600 lbs which will leave you 3200 total payload just considering the tires. The axle rating is likely high enough that you are good for a 4000 lb camper.
Of course, this doesn't mean you aren't overweight from the GVWR perspective. For that number, subtract weights in the door sticker. You can mitigate the tire capacity by going to 19.5s or higher rated rear tires.
'10 Ford F-450, 6.4, 4.30, 4x4, 14,500 GVWR, '06 Host Rainer 950 DS, Torklift Talon tiedowns, Glow Steps, and Fastguns. Bilstein 4600s, Firestone Bags, Toyo M655 Gs, Curt front hitch, Energy Suspension bump stops.
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