Be sure your tires are at the recommended pressures shown on the door frame of the truck. A lot of sway is the result of sidewall flexing with underinflated tires.
Older trucks have frames with 5 times as much torsional flexing and they can benefit from a rear anti-sway bar but it is not needed for the current GM trucks even with a maximum payload in the bed.
A camper puts a heavy load with a much higher than average center of gravity in to the truck. The truck is not going to handle the same as without a load or with a load that is lower than the sides of the box. If you want that then get a popup camper.