Trailer Hitches have certain towing capacity ratings. The commercially available hitch, the EcoHitch by Torquelift Central, is rated at 2,000 Lbs towing capacity (How much you can Pull at MAXIMUM) and 200 Lbs Hitch Load (The MAXIMUM amount of downward force that can be applied to the hitch). After many years, and MANY MANY MANY THOUSANDS OF MILES TOWING, I beg of you, PLEASE DO NOT EXCEED THESE RATINGS! For starters, exceeding the designed ratings of a hitch, and having a failure would most likely be grounds to give your insurance company a "out" and not need to pay out.
I installed my hitch last week Friday, towed a few small utility trailers, towed like a dream, but even though the rating is 2,000 Lbs, I do not plan on towing anywhere near that. I plan on towing light weight utility trailers, never exceeding 1,300 Lbs fully loaded, and eventually when I can afford it, a Teardrop Camper, weighting in at 600Lbs, after Air Conditioning, and gear about 800 or 900 Lbs.
The Model S is not designed for heavy load towing. It's single speed differential is geared for Acceleration and top speed, not for high torque towing.