My 12 Ram 2500 is the same as a 3500 except the rear spring pack. I have 1800lbs for pin weight. I throw other stuff in the bed as well. MY GVW is 9600lbs and I usually weigh in at 9800lbs. A 3500 has a 10,000 GVW. I have Timbrens on the rear so even though they don't technically change numbers they do provide the same or more weight carrying that the 3500 springs would. My rear axle weight loaded is 4900lbs. My RAWR on the sticker is 6000lbs and is tire limited because the truck came with 245/70/17 tires rated at 3000lbs each. I have upgraded to 275/65/18 BFG KO2 with 3415lbs each IIRC.
I also tow a 9000lb 5th wheel making my GCVWR around 17,000lbs+.
My trucks GCVWR is 21,000 so I'm under that by 4000lbs.
I'm only over the trucks GVW by 200lbs and IMO is nothing. The mods I've done have more than increased the trucks payload capacity they also improved it's towing characteristics.
Just me but I'd have no problem dropping 2500lbs in that F250 and my 12 2500 CTD as well.