You don't give any info on your rig, so everyone will be guessing more wildly than normal, or maybe not, but we try to help.
When you talk about sway, I think of truck sway with the camper load.
The cushioned and spring loaded turn buckles won't make any difference in sway with normal driving and turns.
Make sure your tires are fully aired and make sure you don't have too much air in your air springs.(if you have air bags)
The overload springs need to just touch to help with the load.
The one thing that rally helps with sway is a rear sway bar.
Last, if your camper is way too heavy for the springs or tires you'll have sway.