We have a 2012 Avalanche 5.3. 4x4 and pull basically the same trailer. 27ft 2011 Monaco light weight. The gvwr on trailer is just over 6000 lb. Towing capacity of Avalanche around 12000 lbs.
The avalanche is the exact chassis as a chevy sierra, it is the same as a truck according to GM and the ministry of transport and plated so. We have a towing pkg on the Avalanche.
We also pull behind the trailer our boat.
As far as your gvwr is concerned dont go by what you think will be the weight after you are loaded. If you are stopped you will be rated on the vehicle (trailer) sticker weight.
Our Avalanche pulls the trailer and boat with no problem. The dealer suggested the red head hitch with equalizer bars and 2 sway bars.
