No issue with towing capacity on the F250, but tongue weight easily *could* be a factor for the receiver and WDH rating. Assumptions are being made at this point that could get you into trouble later on.
I did a detailed weighing of our new 29' TT last year - on the way home after picking up at our dealer, weight of all mods and weight of all "stuff" loaded into the TT. Actual weight of TT after picking up at dealer was 190 lbs higher than UVW sticker inside TT (after subtracting propane + battery). Weight of all mods was 119 lbs. (shocks, Dexter equalizers, 2nd TV, etc.). Weight of all "stuff" loaded into the TT (sewer stuff, BBQ, food, clothing, etc.) was 555 lbs. Grand total above the UVW sticker was 864 lbs. IMHO, 1000 lbs is a good conservative average round number above factory dry weight to use. Don't forget that if you travel with a full holding tank(s), each tank is 300+ lbs. Carrying FW can change tongue weight a lot, depending on where the tank is. Some owners could drive the weight higher by storing spare tools in the TT, carrying a generator and/or adding a bike rack and bikes, etc. Too many people throw numbers out there (above the UVW) without ever having gone through an accurate before and after weighing procedure, covering everything that is added. And there WILL be variations between makes and models, so there is no standard answer.
I would go with a realistic conservative TT weight loaded up and ready for camping of 9,000 lb. Average tongue weight is typically 12-13% but can sometimes be up around 15% (as in our case). At 13% and 9K GVW, that would be a TW of 1170 lbs. The receiver is probably rated 1250 lbs (using a WDH) and if looking at a WDH rated at 11,000 lbs, it could have a max. TW rating of 1,100 lbs.
You may need to have a WDH with a 1,500/15,000 lb rating (Reese for ex.). You definitely do not want undersized spring bars because you can end up not being able to restore enough wt. back onto the steer axle. Forget about the 600 lb advertised TW. Ain't gonna be anywhere near that low, and will be more like twice that. It's possible you may even need to upgrade the receiver.
At this point, you are purely guessing on the GVW and TW. *IF* the actual TW is above 13%, the actual weight of the TT is more than 9K lbs or you tow with fresh water in the holding tank and the tank is ahead of the axles and/or you want to install a rack for a genny or bikes above the tongue, the actual tongue weight *could* potentially be much higher than 1170 lbs. Not only that, the particular TT being considered has a high CCC, much higher than a lot of other TTs. If you wanted to go on a long trip somewhere, you might want to store a lot more gear, food and other things in the TT to take advantage of the spare CCC. Usually, to be on the safe side when shopping for a new TT, you would assess it by using it's GVWR and applying an expected tongue weight %. So for the Cherokee, that would be 1461 lbs at 13%. I also see that the Cherokee TT is a front kitchen design, which *could* possibly raise TW more depending on how you load it.
I highly recommend that you go to a scale and weigh your F250 to find the actual available payload capacity. Load everything into it you would take on a camping trip along with kids, DW and pets. Subtract that weight from it's GVWR figure. I think you could find that your actual available payload is quite a bit less than you thought - we did with our F250.
FWIW, you don't say where you live, but if towing in mountainous areas like say the west coast which can have long steep hills, you could find the F250 wanting a little more power with an 11K lb TT. I know I do with our 6.8L F250 towing a 7K lb TT. If towing mostly in flatter areas, not an issue.
