I have a 2003 Silverado 1500 with a 5500lb TT. Shortly after we got the trailer, 8 years ago, I replaced the stock P265/75 R16 Bridgestone Dueler's, which would squat under load, with LT 265/75 R16 Toyo Open Country A/T, Load Range D tires and had them siped at installation. The tire's weight ratings exceed the axel limit on the truck, so no need to go to the Load Range E tires in my opinion. They've been fantastic. I've got 76K miles on them and are just now approaching the need for replacement. I run them at 60psi when the trailer is attached or if I'm loading the truck with firewood or something heavy. For standard day to day driving I keep them around 43-48 psi for even tread ware and ride comfort. They're a heavier tire with a slightly more aggressive tread than the stock P tires, so they provide a slightly stiffer ride and my gas milage dropped about 1 mpg (which might be better if I'd gone with the highway tread instead of the all terrain), but I've never regretted that decision. I'd recommend them in a heartbeat.
FWIW.