2200-3000 lbs really isn't enough to make it work hard. With a 16K GCWR mine ran 15.8 mpg on one decently long road trip last summer, with some pretty good hills, 33's, and a heavy throttle foot(I never grabbed a gear on a hill, just made it pull)
With an 18K GCWR on another long towing trip, on a much less hilly highway, I ran 15.7. This is with another F250 on the trailer behind the truck, 33's on the tow rig, 35's on the one on the trailer, and spare parts/tools/etc for a weekend of racing. The second trip was with a real trailer(tilt deck 14K GVWR ... VERY nice to pull) that weighs a good 2000 lbs more than the car hauler I used for the first one.
This is with 3.55's and a 4 speed, with a 2400 rpm criuse, as that's where the power was on demand with the non gated banks.