The more capable half tons will still tow your TT at least as well as your current truck. For GM, get 2015+ for a little more power and payload with the current generation than your 2011. 2014's had a few problems as first model of that generation.
The problem with buying a used half ton is verifying equipment. They rarely come with window stickers showing the exact equipment/options like when it was new. Engine is easy to determine. Axle ratio and HD trailering equipment is harder. GM makes it easier as it puts a sticker in the glove box with the RPO codes to help as you shop.
I towed with two half tons before my current 3/4 ton. At 0-500 pounds over GVWR, the trucks never needed rear suspension help with a well adjusted WDH. If you think you need air bags/helper springs, etc, then you probably should focus on WDH adjustment or buy the 3/4 ton which can handle that much tongue weight without much WD.
The bonus when looking at late model used 3/4 tons is they all have the towing equipment (except maybe towing mirrors which can be switched) for at least 10k pounds. Prices when new were less than $3k apart for same level of trim and equipment 1500->2500 gas. Diesels will be considerably higher as they are another $8k to the gas 3/4 ton which is retained when used for a long time, like 200k miles.