Ah, the TV is designed to carry that capacity. If not, it would have a different capacity listed. I believe my yellow sticker says something to the effect, that I cannot exceed the axle capacities when I stay below the carry capacity.
I remembered I had seen that statement in some of Fords specification brochures and found it. Below is copied and pasted from Fords F150 trailering and towing selector guide for 5th wheels.
Addition of trailer tongue load weight and weight of passengers and cargo cannot cause vehicle weights to exceed rear GAWR or GVWR. These
ratings can be found on the vehicle Safety Compliance Certification Label.
Someone asked the Combined Gross weight rating- for my truck, it's 16,900 pounds. My truck weighs 5,400 pounds curb weight fully loaded, camper weighs a max of 7,000 and my boat weighs 2,300 pounds fully loaded for a grand total of 14,700 pounds.