OK, that pick of the flipped 3/4 ton burb makes me add my own experience. I have owned 4 suburbans, currently own a 99 K1500 and two 2004 - k2500 with the 8.1L. I like it so much, I bought a second one and yes I drive three suburbans, I love global warming but that is for a different thread.
My 3/4 ton burbs pull our 31dbts just fine. (36' overall and weighs in about 10,000 lbs loaded) Went out west past Yellowstone last summer and it did really well. had to slow down on some hills in Montana, but that is to be expected at 17,000 lbs total. I have never towed the TT with the 1/2 ton nor do I want to.
I also own a 272 LS Formula offshore boat and it weighs 8,000 to 8,500 with some fuel and a steel trailer. I often tow that locally in Indiana with the 99 1/2 ton burb with the old 5.7L in it. It does fine with the boat, but you can really feel it back there. Power is OK on the motor as the local roads are only 55 and flat, but the suspension is where it is lacking. And tonque weight as it is just a plain hitch. The boat is much more aerodynamic than the trailer, so that is not so much an issue. I did lose a trailer tire on the boat at 55 mph last summer. Barely noticed it except the vibration and I saw it disintegrate in the mirror. No problem slowing down with the 1/2 ton burb and pulling off the road.
Now I put that same 8500 lbs behind the k2500 burb and it is night and day. That is why I bought the second one. The 1500 will tow the 8500 lb boat, but not nearly as well as the 2500. It is not just the pulling power of the 8.1L, it is the suspension and tires themselves. It feels and controls completely different.
How a 2500 suburban flipped that easily? We do not know all the information, how it was loaded, was it worn out, bad ball joints, who knows. It might have been the truck but it was not because of the truck design.
Tow with your 1500, but if you can upgrade to a 2500, I highly recommend it. It is much better control and suited to getting you there safely.
Just my experience, worth twice what you paid for it!
Good luck.
2012 Puma 31dbts TT
2004 Suburban 2500 - 3.73 - 8.1L - 4x4
Helping global warming at 496 cubic inches per revolution!