Forget about towing capacity of 8200 lbs. That was calculated without passengers and cargo. That's not how we go camping. As you load up the tow vehicle, it's "true" towing capacity is going down.
Your Tahoe has multiple (inter-related) ratings that dictate what the vehicle can carry or tow. It has a payload rating (what is can carry) that, if exceeded, it also exceeds GVWR and very likely exceeds GCVWR, even though the loaded weight of your trailer is lower than that mythical "max tow weight rating".
The reason payload is very important in towing a travel trailer is, the tow vehicle is actually carrying (not towing) on average 12 - 13 percent of the trailer's weight. At times it is higher.
On your drivers door post, there is a tire / loading sticker. It has a number for your particular Tahoe's capacity to carry the combined weight of people, pets, cargo, weight distributing hitch / equipment, and trailer tongue weight. That number will be listed as "max occupant / cargo weight capacity".
Take that number and subtract your families weight, subtract 100 lbs for hitch equipment, subtract the weight of any aftermarket accessories added to the Tahoe, and subtract weight of car seats, luggage or anything else you would carry in the Tahoe. Whatever you have left is payload capacity available for carrying tongue weight.
Once you know what your capacity is to carry tongue weight, divide that number by .13, and that will be a ball park number for loaded trailer weight that puts you Tahoe at, or near, it's payload capacity and it's GVWR. Say for example, you have 700 lbs payload available ---(700 divided by .13) comes out to 5385 lbs of loaded trailer weight. An 8200 lb trailer would need 1066 lbs available.
When you go trailer shopping, keep in mind, sales people will be talking unloaded (UVW / dry) and gross (GVWR) trailer weights, neither of which are you likely to be towing. They do that because they have no idea what you're going to carry in the trailer. Only time you'll be close to UVW is when you pick up the trailer from the dealer. The average load is 800 to 1000 lbs, and that is usually below what the trailer could carry.
Give yourself some cushion because (1) the closer you get to max weight, the more unpleasant towing will be, and (2) tongue weight is not a constant number. It fluctuates up and back down, during every trip.
You're looking at trailers that are in the right weight class and should be good to go, unless you've underestimated your cargo / passenger weight, or, unless your Tahoe has a low payload capacity.
Good luck
