First post, first TT, first of many stupid questions.

Sway is an entirely different problem from towing capacity. It's possible to sway your way off the road sideways with a 1500 lb trailer that is bad, yet drag straight as an arrow a 6000 lb trailer that is well designed and set up properly.

That being said, I'm going to guess that your first problem is that the truck's rear tires are under-inflated. This rig, at a sticker weight of 5,828 lbs, behind a TV rated according to the sticker on the door at 6,000 lbs, is right at the limit. So I think you have too much trailer for the truck.

But beyond that, if things were set up right, your main problem would be accelerating, stopping, and going uphill, not swaying.

Assuming you have the right tires on the TV, you can't load it up like that and NOT pump up those tires, especially the rear ones, to much higher than you run with the truck empty. If you failed to do that, the fix is obviously really cheap. At least as a first step.

GVWR is 6,600.

Weight Distributing Hitch is brand new and installed by dealer.

Sway bar, the same.

Tires are brand new, as in, the day I bought the trailer.

The dealer says that the length isn't relevant.

Thanks.

Do you have a WDH? Sway Control? How much does the TT weigh when loaded?
How much does the Tahoe weigh when loaded? What is the Tahoe's GVWR, GCWR?

Look on the driver's side door jamb for the sticker that lists cargo and passenger weight. Report back, you are probably overloaded.

Other things that can effect sway---Lack of weight distributing hitch or no provision for sway control installed. Weight of tongue is not correct, maybe influenced by loaded weight of stored items in back of trailer. Tires not inflated correctly. Soft tires or suspension on towing vehicle.

THat trailer is 30' long and it may be a case of the tail wagging the dog. Tell us what WDH and sway control you have installed.