My turn to give you numbers. Then you plug yours in.
+ F-150 with max cargo from door sticker 1411 lbs.
+ Two adults and dog 500 lbs.
+ Truck cap 200 lbs.
+ Camp gear and stuff in bed of truck 100 lb.
If you do the math it leaves 600 lbs for tongue weight.
The dry weight on my TT is supposed to be 5000 lbs, the CAT scales indicate the loaded weight is a bit over 6000 lbs. So the DW and I have added about 1000 lbs in food, cloths, bedding and camping stuff.
I suspect you numbers will be similar, so you may be over you TV cargo limit.