I have the 2013, 2500HD, 2WD, CREW CAB.
I can't attach a pic, but I got 3,037 exactly, from page 11 on the 2013 Chevy PDF. You can look at it at http://www.chevrolet.com/content/dam/Chevrolet/northamerica/usa/nscwebsite/en/Home/Help%20Center/Download%20a%20Brochure/02_PDFs/MY13%20Silverado%20HD%20eBrochure.pdf
I could easily be mistaken because those charts get confusing. :)
My GVW is 10,000 but I can't figure out what the truck weights. I assume it would be the 10,000 less the cargo capacity.
I have a 36 gallon tank so fuel would be roughly 288 lbs, I weight 250, my dog weighs 50 (and he never lies about his weight ;) ), I'll assume 80 lbs for the hitch, and 100 lbs of misc tools, etc. If my math is correct, that's 713 of cargo....subtracted from 3037 would leave 2,324 for a pin weight plus whatever portion of the trailer's cargo weighs on the pin.
Does that sound right to you?