You are 100% correct. There's some bad information floating around on this thread.
Unfortuntately, what you're finding out is that a half-ton Suburban/Yukon XL is not the towing beast a lot of folks make it out to be. I remember when I bought my first Suburban, a 2001 1500, I drove over to the RV dealer and the salesman came out to me and said, "Great choice. That truck can tow anything. Pick whatever you want on the entire lot." Well, three busted rear axles later and I sold it to a buddy and bought a 2500.
The problem with the half-ton trucks, as you're finding out, is the payload. You have 1500 lbs for you, your other passengers, gear, hitch (don't forget that weighs 20-30 lbs), and trailer tongue. If your passengers and gear weigh a lot, this reduces what you can tow dramatically. When we first started towing, my 3 kids were small. We also had a trailer that was about 4550 dry.
Then, as the kids grew, we upgraded to a 7,000-lb trailer. Here's where the problems started. On several long trips, I killed/overheated the rear axle to catastrophic failure.
So that's when we bought the 2500. Instead of 1500 lbs of payload, I have 2100. Instead of a 4000-lb rear axle rating, I have 5500. And so now, I tow this (8600 lbs loaded):
When we started towing, our family weighed about 600 lbs, with my fat a$$ being almost half that. Even though I lost a bunch of weight, the kids all grew and now we're 950 lbs.
So here are the critical numbers, this is from my last road trip out to Wyoming last summer:
My vehicles ratings:
GVWR 8600
RAWR 5500
GCWR 16000
My Gross Vehicle Weight? That's easy. That's the weight on the four wheels of the truck. 3080+5500 = 8580
Rear axle weight? Even easier. 5500. Hey, look at that, am I good, or what? Actually, I'm not concerned because the axle in my truck is rated to 8600 lbs by the manufacturer, American Axle, and my tires can each carry a max of 3000 lbs, so I'm not overloading anything.
Gross combined weight? Simple, add them all up. The slip already did that - 16,160. So I'm a bit over on my GCWR. Not a big deal.
And regards to weight distribution - be careful. If you take too much weight off the tongue, it tends to make the trailer more prone to sway. I did that exact thing with my half-ton, trying to get weight off the rear axle. It made the rig much more prone to sway and crosswinds and getting passed by trucks was a constant adventure.
Endeavor to put as much gear in the trailer as possible, but you still want to aim for 13% tongue weight. Anything lower and you increase the likelihood of sway. So if you have 500 lbs for tongue weight, 500/.13 = 3,846. That's not much. But every pound of gear you can move to the trailer gets you seven more pounds of trailer weight. So move 200 lbs into the trailer, and now you can handle a trailer up to 5,385.
Lastly, about that rear axle. It's a semi-floater, as compared to the full-floater in my 2500. You can do some Googling if you don't know the difference, but the main thing is that the semifloater works much harder to do the same job. It has to carry the weight AND transmit the torque to the wheels. In a full-floater, the axle housing carries the weight and all the axle has to do is transmit the torque. Big difference.