It's a 2500 Sub, not your average grocery getter.
Sidecar, how did you end up with an '08 Sub with a 350? They quit using those back in about 2000. If it's a 1500 it has a 5.3, if it's a 2500 it has a 6.0.
OP, I have a '09 2500 Suburban. I use it to tow my boat. I haven't weighed the boat on the trailer; the boat lists a dry weight of 4,100 + 75 gallons of gas = 4,625. Adding the trailer and all the gear in the boat I must be around 6,000 to 6,500.
I have no issues at all towing this trailer with 7 people and gear in the Suburban. I can go over the mountains of VA at the posted speed limit with ease. I have power to spare.
My '09 does have a 6 speed where you have only a 4 speed so I probably have an advantage there. I wouldn't be concerned with another 1,000 or so pounds behind me. Granted, a boat tows much easier than a TT but as for weight, I don't see it being a problem.