If it helps, I also weighed the truck yesterday at a CAT scale. I filled it full of gas and weighed it with me outside of the truck. Here is the actual truck weight:
Steer Axle: 3060 lbs
Drive Axle: 2240 lbs
This is all you need to figure how much weight any truck can safely carry. Your math (3350 minus 2240 lbs = 1110 lbs is your trucks rear axle payload. Your F150 has a very small 3350 RAWR
Was the 2240 lb with everyone and gear in the truck ?? If not don't try and estimate the trucks numbers when you can load it up road ready and then weigh and use those numbers. It may surprise you how occupants in the cab affects axle weights different than you may think. People's weight in the front seat won't all go on a trucks front axle.
The 3350 GAWR is the smallest of any 1/2 ton trucks out here.
The F150 does have around 12-13 different GVWR numbers and ;
3800 RAWR
4050 RAWR
4550 RAWR
4800 RAWR (HDPP)
As you see your looking at a very small TT vs higher rated F150s.
My biggest concern at this point is "how do I estimate which RVs have a trailer hitch weight I can support?" I know this will be an estimate, but I want to be careful I don't overload my truck from the start. Is 14% of the trailers GVWR a safe assumption for purchasing? Or any other advice to estimate this?
I use the trailer mfg dry gross weight numbers...CCC numbers...GVWR numbers. For a trailer that size your not going to carry much like some one with a 30-35' TT or 5th wheel trailer.
A 4000 GVWR trailer may have a 2800 lb dry weight. Now add 700-800 lbs in the trailer = maybe 3500-3600 lbs gross weight.
Using a 10 percent hitch weigh = maybe 360 lbs. These are estimates so I use that type of math for a 5k-6k gvwr trailer.
AS the trailer gets bigger we tend to carry more necessary Junk :B