Do not go by the manufactures tow rating when looking at a 1500/150 series truck!!! They are a marketing number only.....
Look in the drivers door jamb of all vehicles built since '06 (think it is). It states, "All passengers and cargo not to exceed XXXXlbs". As it states, all the passengers in the tv, all cargo (coolers, firewood,bikes,etc), any accessories added after the truck was built (truck topper/tonneau cover, step bars, etc), the wdh (weight distribution hitch), and the tt tw (travel trailer tongue weight).
As an example: our last tt weighed ~7200lbs loaded, ready to go with ~920lbs tw. Our last truck, with the family (~475lbs total or so), about 200lbs in the bed: cooler/4 bikes/tool box/leveling boards, bed liner, cab high truck topper, the wdh, and the 920lb tw, we were over gvwr by about 200lbs. Combined was just under 14klbs. The gcvwr was about 16klbs I think for our '10 Chevy ccsb 1500 5.3/6spd/3.42 4x4. As a result, we bought a 2500HD, then 2yrs later ended up buying a new trailer, that was bigger.... Lol