With the Ford F-150 Heavy Duty Payload package you can get a truck with a payload rating of 2900 lbs., and it has 18" rims and tires which is where you get the higher load rating. Load ratings on stock pickup trucks are based on the weakest link and that is always the tires.
With Ford I would want the F-350 for towing and get the stronger frame provided with this truck as well as better brakes. I would also go only with the V-8 engine and the 4.30 gears for towing.
In the 2500/3500 class of truck Ford would be my last choice. Much greater towing capacity with the Ram pickup trucks.
The alternative is to get a trailer with a GVWR of 7,500 lbs. or less and these are not difficult to find. The trend is toward lighter trailers that require less power to tow so that people can have better fuel economy.