I beg to differ with Naturist. I have an 05 Suburban 2500 with 4:10 rear, 8.1L engine, and full factory tow package. It is rated to tow 12,000 lbsand a 19,000 GVRW & pulls and stops my 38' 9,000# trailer just fine.
I traded my 2010 Ram 2500 CTD for it because I needed to carry more people that the pick-up would carry (7). The rating is only 1300#'s less than what I had in the Ram, but what I do miss is the torque of the CTD & exhaust brake. Other than that, no issues whatsoever. Just had it through the CAT scale fully loaded on a trip and was well within all specified ratings.
The only issue that OP may find is that Chevrolet doesn't make the 2500's anymore, and used ones are fairly hard to come by, when they do go up for sale, they go quick. That's a shame because there are families out there that like to camp, but are larger than the people carrying capacity of a pickup.