I tow a 29' trailer that is less than 8,000 lbs, but with a tongue weight of 1200-1300 lbs per my Sherline scale. Mine is a 2003 Suburban with 4.10's and the 8.1L. It tows great. I use a Reese Dual Cam system and it works great. I did replace my hitch with a Class V Reese with the 2.5" square tube opening. I liked it because it mounted further up along the frame than the stock hitch and the other options. I don't think they make it anymore however. Regardless, I'd replace it with something better than the factory one, it was pretty weak regardless of the ratings they put on it.
Mine started life in a Fire Dept. in Georgia from what I can tell, then an owner in Florida. A previous owner had removed the auto ride shocks and put on Rancho 5000's that were worn out when I got it. I put on Bilstein 4600, they work very well. I also added Hellwig sway bars front and rear on my Suburan. It significantly reduced body roll and I believe provides better control when towing also. I've towed to most of the states in the lower 48 with this combination and it tows great, even with 20-30 mph cross winds. We traveled 5000+ miles out west this summer and it did great.
I've relaced a LOT of parts as it is an old vehicle. All coolers, lines, radiator, etc. Fuel pump, water pump, etc. I've also replaced the accelerator pedal assembly and more recently the throttle assembly as the electronic controls and sensors go bad eventually and it leaves you in low power mode. Low power mode will not move a loaded travel trailer and hardly move an empty vehicle. We nearly got stranded due to the throttle issue this summer on our last day. It eventually started working and we made it, only because I could re-set the Service Engine Soon light on the fly.
Good luck with yours, it pulls fine over the mountain passes if you keep your speed up and keep the RPM at the power peak (4200 RPM). I think we did 60+ over Vail pass as we were unhindered by traffic. If you slow down you'll never get your speed back up, we ended up in 1st gear approaching the Eisenhower tunnel due to traffic.