Jbres, the Suburban will handle that trailer fine. Big difference in going to the 2500 series from the 1500 series Suburban and Tahoe is the suspension and brakes. 2500's get rear leaf springs and front torsion bars, same as the HD pickups, while the 1500s have coil springs and are set for comfort more so that towing a load, which is why you feel like the trailer is controlling the Tahoe today. The 2500's also get massive disc brakes at each corner.
When you say tow rating is "only" 7700 lbs that's a more a function of drive train....my Sub is rated at 12,000 lbs towing and has the same frame and suspension as the one you are looking at.
The 6.0L is no powerhouse though....better than the 5.3 but not as strong as the big block or diesel. As I said for your camper you will be fine, but if you have plans to get a bigger/heavier TT in the future, you will be upgrading the truck again.
