I've got pretty much the same getup (Silverado), with a Hypertech program, K&N cold air intake & a Corsa cat back. When the truck had about 7,000 miles on it, I put one 2,500 lb. pallet of coal in the back, then took my enclosed trailer (probably 1,600 lbs.? empty) & put 2 pallets on that ...... so 7,500 plus 1,600. Pulled it up a long, steep hill at 45 mph no problem. Owners manual says 7,500 max towing, but I've never been one to follow weight ratings.
But then again I only had to go 7 miles.