First, is that pin wt from manufacturer data? If so, it is based on an empty FW and absolutely not correct. Find the GVWR for the FW and use 20% - 22% of that as a much better pin weight estimate.
As a good general rule, F150 can not pull a FW. There are exceptions.
F250 can pull a SMALL FW, less than 12,000# GVWR. Not enough Payload for a bigger FW.
F350 SRW should handle FW up to 15,000#.
The best way is to get a good estimate of pin wt. as above. Add 200# for a hitch. Add the weight of all passengers, pets and cargo in the truck. The truck Payload, or CCC must exceed this number. This number, by definition, is truck GVWR minus actual weight. There is a yellow label on the driver door B pillar for THAT TRUCK as it left the factory. YOU MUST CHECK THIS FOR EACH VEHICLE.
I have a 2013 F350. For that year, there are 50 unique configurations, each of which have unique payloads for the base model. Factors include the truck GVWR (one option is a reduced rating), cab, bed, 2WD or 4WD, which motor and even tire size. Larger tires have higher load carrying capacity. From this number, you must subtract the weight of all options and accessories.
A 13 F350 just like mine in XL trim with no options has over 500# higher CCC than my Lariat has.
I tell you this, not to confuse, but to show why it is so important to look at the yellow label on EVERY truck you consider.