So much conversation and debate. This is just as much a philosophical quesiton as it is an engineering one. Is a given trailer too much weight for a truck? It's already been discussed in this and a zillion other threads. The truck can tow so much. The axles can hold so much. There is GVWR, etc. All you have to do is run the numbers. Take 25% of gross trailer weight and that should be about the most pin weight you can expect for a given trailer. Run the numbers after you weigh your truck and you can calculate and answer your question. If you don't have the truck yet, some research can show you about how much they weigh over each axle for a given configuration.
The philosophical debate is what happens when DMV in various states forces us recreational truck users into commerical policies when we purchase a truck over 10,000lbs GVWR. It's one of the primary reasons the 3/4 tons exist. At 10,001 lbs, in NC, you have to go commercial. For me, that meant losing my multi-car discount and an additional $900 for a commercial policy. That was $1,200 extra per year. So I purchased a 250 and added air bags with an on-board compressor to bring up the rear when I'm hooked up. It's a silly rule. I am towing a camper that I use 6-8 times per year...which is a recreational activity. I should have been able to purchase the 350 without that insurance penalty for how I use it.
For the OP, remember that you can't go by what truck manufacturers print for payload capacities. That assumes you have the shortest lightest Super Duty they sell. Each length/configuration adds weight. Each option adds weight. All of that steals from your available payload capacity. For instance, a gas F-250 may have 750+ lbs extra payload over a fully optioned 250 diesel with 20" rims because the latter truck weighs so much more. Truck's weight minus 10,000 lbs on a 250 is what you have left for payload -- and remember that passengers, fifth wheel hitch, and of course pin weight all have to be accounted for. On such a heavy truck, you can blow way past your 10,000 lbs easily. Does that mean the truck can't handle it? No. You will likely be under your rear axle rating if you stick to a trailer with a gross of 12,000lbs or under. But will you be over GVWR? Yup...sure will if you approach that much trailer. Will the truck care? Probably not. Will the DOT care if you were sent to the scales? Yup...and they'll be happy to drain your wallet of all remaining cash. The latter is unlikely to happen unless you LOOK overloaded. But again...it all comes down to the numbers and how comfortable you are. I would think an 11,000 - 12,000 lb trailer could be handled by the 250/2500 pretty easily with some air bags depending on pin weight...but you will likely exceed your GVWR.
The conversation can go on and on. BOTTOM LINE: You will never be sorry for having too much truck.
- DNC