Presuming you have adequate tire pressure especially in the rear tires and the camper weight isn't sagging the suspension too bad (I'm pretty certain it is since you don't have any suspension upgrades and I have the same truck, 2500lbs in the bed is on the upper end of what the factory coils are good for.) then it's because of the type of rear suspension.
Geometrically, the coil sprung Ram 2500s are not a good fit for high center of gravity loads. Period. In short, it's the "wrong" type of suspension to haul a TC of any real size.
That said, there are a few upgrades that will help considerably. Although idk how many firsthand reports you'll get since you don't see many TCs on coil sprung 2500s (due to your issue).
1. Put an aftermarket sway bar on. Regardless of truck/suspension type, this is the first step to controlling body roll that you're experiencing. Super easy diy install.
2. If that doesn't do it, depends on the load like I said above. Then you need additional spring capacity. 3 options, heavy duty coils, Timbrens, or air bags. I wouldn't probably consider Sumo springs as they're a bit soft. My first choice (and the easiest and cheapest) would actually be Timbrens in this situation. They all mount outboard of the springs which helps with roll stability and timbrens are pretty stiff when loaded. Maybe too stiff, but you want to control body roll, not ride in a Cadillac.
3. Or maybe this is #2, a stiff set of shocks. I've only used Bilsteins, some say Rancho 9000s are stiffer. I'd maybe think past these and step up to some real heavy duty shocks like King or Fox and have them valved stiff and slow on both compression and rebound.
Lots of improvements available and I think you'll end up spending some money to work around this type of suspension. Good luck.
