I also towed 7,500 pounds with the 5.3, 3.42 (2013 Silerado) and had no complaints. I took that combination through the Smokies and Ozarks, but not the Rockies.
I upgraded to a 2500 because I bought the wrong cab configuration and decided if I was upgrading, I would buy something that could hold a rick of firewood in the bed while being hitched up. I don't do "RV parks" with full hookups, and I need a rick of firewood and an extra 50 gallons of water in the bed of my truck for three or four nights of camping.
Look, if you listen to most of the posters on this forum, you will end up buying a Mack truck to tow a popup.
MY FIL has a 2013 Sierra with the 5.3 and 3.42, and he tows a Windjammer that is 35 feet long and weighs 8,500 pounds. He upgraded the tires and has taken that combination all over the country, including the big mountains out west.
People used to tow much heavier trailers with vehicles much less equipped than those we have today. Decide what you are comfortable with, but don't put a lot of stock in the "go bigger, no matter what" posters on this board.