stronger rear end

You said "WE", so the max specs don't apply. The "specs" are for a single driver, in a stripped truck. All weight (spare tire, back seats, etc) added beyond that, and don't forget the passengers and all carry on luggage, as well as the hitch are added to the weight of the truck, which comes off the "specs" weight you can tow. Your best bet - if wanting to stay within "specs" is to load the truck as if you were going camping, put the hitch in the receiver, and go hit a public scale. In this case, the only spec you are working with is GCVWR (the max weight for truck and trailer). Take the scaled weight and subtract it from the GCVWR, that is the MAX weight - dripping wet - of a trailer. Assume the trailers dry weight / shipping weight is a figment of someone's imagination, and go with the gross weight. Assume 15% of that is on the TV as pin / hitch weight. Is the rear axle within specs with 15% of the gross trailer weight? Is the truck within spec with 15% added to it?