I'd guess your springs could be soft, with Age and Mileage. Does one end ride lower than the other? If the Rear is low, then those springs are tired and sagging.

This is a sample pic of a rear anti-sway bar from Hellwig, which is an excellent provider. The bulge in the center of the bar in the photo is to clear the differential. The two portions outboard of that bulge, parallel to the top edge of the photo, clamp to the Axle using the hardware in the center of the photo. The remaining four pieces link to the chassis. The idea is that for the vehicle to sway or rock, the Sway Bar must be twisted, in addition to flexing the springs. On RV's, notably Class C's, Front and Rear Sway Bars are very successful in improving both road manners AND stability when stopped, parked, camping.
If you're driving what I think you are, Hellwig offers front and rear sway bar kits. More vehicles come with a front bar than a rear bar, and often the front bar is puny. So it's not unusual to Replace a Front Bar with a better one, and Install a Rear Bar where there wasn't one before. The improvement is stunning. They cost about $200 each.