Just got through looking at the tires on my 2011 Silverado: Bridgestone Dueler AT RH-S, P265/65 R18. Rated to maximum of 2468 lbs at 44 PSI. NO load range stated that I could find. In my 46 years of living on the same ranch, the Bridgestones do the best at holding up to our mile-long driveway of caliche and rock. I've tried 'em all, Firestone, Goodyear, Michelin, you name it; all the tires on my trucks failed early, usually showing missing chunks of tread; compared to the Bridgestones. By failing early, I mean having to replace them at 30K miles. The Bridgestones usually get me 40K. Current ones have 22K and look like they'll make it to 40K fine. (Our ranch road has some pretty good hills, meaning that I'm in 4-wheel-low when coming or leaving with a trailer weighing 5K or more. We had a diesel mechanic come fetch a JD 450C crawler loader that died on the back of the ranch, his heavy Ford F550 with dual rear wheels couldn't get the 9-10 ton trailer with machine up the main hill; luckily our deer hunter was nearby and hooked his 4WD Silverado on, and the two trucks could haul the load up the hill. ...)
Main point, it does not hurt to check TV tires, and TT tires, to be sure you are within recommended parameters!
2014 Chevrolet Silverado 3500HD Crew Cab, long box, Duramax and 3.73, SRW
Equal-i-zer 1k WDH, 2013 White Hawk 27DSRL
Los Madrones, a little slice of Texas hill country heaven