Maybe the window sticker shows your trucks payload.... Look again in the drivers door jamb (or on the door itself) for: http://www.f150forum.com/attachments...on-sticker.jpg
If the loaded tt weighs ~8000lbs, you could have a tw of ~960-1200lbs (12-15%of loaded trailer weight). Some trailers like more, others are happy at the lower end. But you should be somewhere in that area for a safe, stable tow. Having to light of a tw can, and usually causes sway to happen.
As for your truck with the 3.13 gears towing ~8000lbs, hard to say. That is something you will have to see what your truck is rated for, and how it does.
Is the tonneau cover a fiberglass or vinyl model?