You can not load up the Tahoe and still carry the maximum tow rating that GM published with just the empty option free Tahoe with a 154 pound driver inside it.
The GCVWR might be say 15,000 pounds (my guess based on a typical truck weight of 7,000 pounds and you stated it has a 8,200 pound towing capacity). So if the curb weight is 7,000 pounds and GVWR is 8,500, you have about 1,500 pounds to work with (check your actual weights and weight ratings) so if you have 800 pounds in additional to the empty curb weight of the Tahoe, and add 700 pounds of hitch weight, you will be at your limits. This leaves you with only about 7,200 pounds left over when the curb weight of the Tahoe is 7,800 pounds (packed with camping gear and it's 75 pound weight distribution hitch too).
So you should be looking at 6,200 pound trailers with less than 750 pounds hitch weight. Then once you add 50 gallons of water (300 pounds) and camping stuff (cookware, plates, silverware, clothing, hair dryer, and all that stuff) and 150 pounds of food and spices, you will still be under the 7,200 pounds that can be towed when there is 800 pounds of stuff inside the Tahoe.
Good luck!
Fred.