Just FYI, my F-250 Lariat crew cab, 6.2L gas, 6'9" bed, 4x4 (but not FX4) with 18" wheels (with all-terrain tires), completely stock, has a door jam capacity of 2700lb, and iirc that's supposed to account for a full tank of gas (35 gallons) and 150lb for the driver (yeah, right!
In my case, if I take off that 150lb allowance, and add the weight of all 4 of us (say 580 lb total), that leaves me with a capacity of 2270lb
My hitch and rails weigh in at about 190 lb (that's shipping weight for both, so no doubt a little lower in reality), so add that to the weight leaves 2080lb capacity
The pin weight of our fiver (one of the heaviest pin weight "ultra-light" trailers around) is around 1600 lb (unladen), leaving us 480lb "spare" capacity
Also remember that for most trucks the listed cargo capacity is artificially limited by the 10K GVWR "package" (just a regulatory thing so that the truck is not officially rated above 10K capacity for taxation reasons iirc) ... not that I'd suggest exceeding that capacity by much.
While the F-250 has been great towing our fifth wheel, I don't think I'd want to tow anything substantially heavier with it, not without modifications at least, purely due to how much the bed drops when hitched. Don't get me wrong, there's still plenty of clearance over the wheels, but I just wouldn't want a rough ride.
On the subject of ride, it's not the smoothest, but not too terrible either. I just wish I could prevent the front-to-back "chucking" (which tbh I think is due to the hitch head sliding back and forth on the mount it sits on (It's a Reese Titan 16K)), and some of the road bounce (which I guess is just having truck suspension).
I haven't actually weighed my truck/5er setup, and tbh have never had any experience using a weigh station (so any advice would be appreciated, IM is fine).
I hope some of this info/feedback is helpful to the OP.