A couple of times you say sway bar, singular. There should be two antisway controllers for this setup I'd suggest. You may want to tighten the tension bolt down a quarter turn, check the clamp rod is tight.
You say tire pressure was checked, but was it checked to be the maximum that is rated for your tires (as suggested by others), as opposed to the door plate pressure. This makes a big difference others have noted.
I notice in the trailer specifications that trailer has a dry hitch weight barely more than 10%. With that solid suspension and strong hitch you have room to put more weight upfront in the trailer as you may be lighter than optimal, see if you can add say 200# of stuff at the front and see what the effect is. Not enough hitch weight is a prime cause of sway, which is the opposite of what some people assume when first starting out.
Tahoes are high ride height, solid axle, and have poor overhang ratios given their much shorter wheel base than their truck heritage had. They can be made to handle ok, but you are starting off from a non-optiminal situation. Make use of that strong suspension by getting some more weight forward if you can, the problem is fixable.
The setup may not have been done properly too, does the Tahoe sit level with the trailer on? Are the two weight distribution bars roughly horizontal to the ground?
