SRW TC size/weight limit

I hauled an 11' Fleetwood on a 2007 Chevy SRW 3500. It was an older model camper so it had no basement and no slides. Loaded up to camp it put about 4,500 pounds on the truck. I was right at the limit of the rear tires. I added airbags and drove it thousands of miles without incident. Your truck is even more capable due to it's improved frame and springs from an '07. However, I would try to stay with no more than a 9 or 10 foot camper. Modern campers with basements and slides are a lot heavier.
When I put my 11' camper on a 2005 Chevy dually after a few years the difference in ride and handling was incredible. It was a much, much nicer experience. Less bounce, less sway, better ride, etc. The dually isn't a slight upgrade, it's a monumental improvement.