We tow about 6500 pounds wet weight with a 5.3 Suburban, 9th gen, iron engine. Fully loaded were probably a bit heavier than that. The Suburban chassis with Sumosupersprings handles the weight awesome. The WD hitch with the Suburban length is a good combination. The 5.3 is OK. The thing I had to get use to was RPMs. Don't let the transmission decide what gear to be in all the time. Most of the time it's OK. But, when pulling long grades make sure not to allow the engine to lug. If the RPMs drop below 2k gear down and get the RPMs up. The 5.3 makes it's horsepower at higher RPMs. On mountains I pull it down to 2nd gear (I have the 4L60e with 3 speed and OD). I can actually accelerate pulling the trailer up a mountain and my RPMs are around 3500, depending on speed. I usually stay around 50 - 55 on mountain climbs, but the power is no problem.
I cannot speak to the shorter chassis on the Yukon. I see Yukons and Tahoes pulling trailers at the campgrounds. Get your WD hitch set up by a professional who does it all the time. It will really make a difference to have that as perfect as possible. We have never had an issue with trailer sway with the burb and the new trailer.
I drive easy. I try to make life easy on the transmission. I sometimes use tow/haul and sometimes not, depends on how it feels and the conditions. Torque converter lockup is what you're looking for. On tow/haul the transmission is designed to quick shift so, the shifts can feel kinda harsh, they do to me anyway. So, I pull off from stops easy.
We got home yesterday from our annual holiday trip down the coast. The Suburban did awesome. We cut the trip short by a day due to the frigid temps at the beach and a couple other issues. Nevertheless, when I decide to trade the Burb I'll get another Suburban or an Expedition.