From what I have been able to gather, my current F 250 crew cab, 4x4, diesel weighs just over 7000 lbs according to those who have weighed similar trucks on scales with fuel. I also carry a toolbox, gooseneck hitch etc but the bed is otherwise empty most of the time. I probably have at least 200 lbs in chains and binders in the tool box. Probably 200 lbs in hand tools and too much other crap to mention in the tool box. My toolbox is a large chest and I don't even bolt it down to prevent theft. I just lock it if needed. I would guess it weighs about 500-600 lbs. If they can lift it to steal it, I couldn't stop them anyway.

Add myself and a couple of other people and it is easy to get over 8000 lbs.
I got ticketed at a weigh station once pulling a trailer with a Kubota
B7100 on it - a subCUT. The trailer was rated for 7K and was easily under the limit. However, I got ticketed on the truck because it weighed over 8000 lbs. (noncomercial plates at that time were rated for 8000 lbs) That truck was a F250 v10 gasser, crewcab with less tools in the box back then. I probably had the tongue weight on the trailer a little too heavy and probably near 750 lbs because the tractor was a little closer to the front of the trailer than needed instead of over the trailer axles. I was the only person in the truck. I think my total truck weight was about 8600 lbs. After that incident I got farm plates and now can haul up to 26,000 lbs on the truck and trailer combined.
I used to have a 2003 Corvette (aluminum block, fiberglass body etc.) which had a curb weight of about 3400 lbs. It would seem your F250 should weigh more than 4000 lbs.