We had a '02 Chevy 1500 Suburban. It towed our pop-up just fine, but when we got our first TT, it took no time at all to destroy the transmission (I'm talking less than 3 months). We had the transmission replaced with a rebuilt transmission, but it never drove the same again. We ended up trading for a 3500 duly.
Click on my "profile" to the left and you'll see a photo of it. There is nothing you can do to improve the towing capacity. If you are looking future bound, start considering NOW for a 2500, or a 3500 while your current Suburban may still have some resale value (if any at all now).