The first thing you need to do is figure out the max. payload and what the max. weight of trailer is before you consider a TT's quality and weight.
As already said, you will run out of payload before you reach towing capacity. Do NOT go by the advertised payload capacity or what is on the door jamb sticker. And anything you've added takes away from the payload capacity, as does a WDH of about 100 lbs. If you've added a canopy, that's around 150-200 lbs. Since you say your towing capacity is 7900 lbs, it looks like you have model no. 8339 according to this Toyota data:
2012 Tundra towing specs. Payload capacity is shown as 1315 lbs.
If you use the Toyota payload figure of 1315 lbs (which may/will be less) subtract an average weight of cargo, passengers, pets, groceries, camping gear, firewood, etc., of 400-500 lbs and 100 lbs for WDH. Using the 500 lbs for total cargo wt., that leaves you 715 lbs of available payload capacity.
Tongue wt. can vary between 10-15%. Don't use an average of 12%. You will have NO idea what it will actually be until you buy the TT and weigh it. Tongue wt. on our TT is slightly under 15%. Take the 715 lbs payload. cap. and divide that by 0.15 and you get 4767 lbs for max. gross weight of the TT you can pull without overloading it. If you happen to end up at the low end at 10%, you'd be able to tow up to 7150 lbs max. actual weight. 12% = 5958 lbs.
Forget about factory listed dry weights. Never, ever use them for a buying decision if TV capacity is a concern, You can end up in serious hot water afterwards. The actual weight of our TT is 200 lbs under the GVWR and we only have some very ordinary stuff in it for camping. Always use the GVWR unless you know
for certain what the actual wt. is going to be.
Additional weight of cargo you add to a TT, things you may add (2nd TV eg.) and things the dealer installs adds weight. Around 1,000-1,500 lbs. typically. For two TTs in a row (20' & 29') we've been at about 1500 lbs. Using the 1500 lb figure, and using the "average" tongue wt. of 12%, that gives you a dry wt. of 4558 lbs. as a max. wt. you can shop for. Not a heckuvalot....
GCWR may not be an issue, but I would also watch that too. Another thing is you want to avoid towing near the max. towing capacity. It won't be pleasant towing. You'll be slow to accelerate and will be a dog on hills. I doubt you'll end up anywhere near 7900 lbs tow max. though.
You really ought to go to a CAT scale and find your TV's weight. And when you get a TT, same thing.
Since you are going to end up weight restricted, you will probably end up looking at ultra-lites. Be wary. Very wary. Ultra-lites are of less substantial quality overall in order to save weight. Everything in them is "minimalist". This means they will be less durable and more prone to problems. Some of them now have an I-beam made from 3 pieces of sheet steel (lengthwise). These have more flex in them than the typical forged I-beam and can lead to some serious problems down the road.
Forgetting about TV towing limits, I would look at either Outdoors RV or Northwood products for best quality. People love their Outdoors RV units and I have only read about minor warranty issues. Quality means a weight penalty though. These two manufacturers also make their own frames. Substandard quality in the TT industry is the norm unfortunately and the trick is finding one of better substandard quality.
