The dry pin weight is listed at 2525 lbs, so the truck's payload isn't an issue. The dry weight/GVWR is 15585/18000 lbs. The 2010 Trailer life Towing Guide (I can't get the 2009 guide to load) indicates a max tow of 15900 for CC DRW 4x4 with 3.73 gear ratio...the EC and RWD are slightly more. The only way to increase the towing capacity would be with a higher gear ratio or more power via an engine tuner.
If you look up the same combo for 2011 when GM increased the output of the Duramax, the max tow rating increased to 21000 lbs.
Nights camped in 2013 - 55, 2014 - 105, 2015 - 63