"Wet" weight does not include your stuff, only propane and fresh water. A family of four can easily add 500-1000lbs of stuff to even a small truck camper. Unless you're a family of nudists that just sit on the ground cold and hungry at your destniation.
It also does not include optional equipment such as the air conditioner.
One universal truth of camping: It weighs more than you think it does.
The camper you are proposing on an F150 is just not feasible in the long run. An F250 would be a much more prudent choice, though still pretty heavily loaded, it would not need many/any modifications while you'll end up throwing thousands of dollars at an F150, throwing away a perfectly good set of tires and wheels, etc..