Any weight added behind the rear wheels of a trailer will likely increase sway, whether added to the tail end outside or inside of the trailer. The physics of the added weight and the extent of its affect can be calculated for those who so care to do so.
Best way to combat it - install a Panhard bar (aka track bar) on both axles, and make sure your tires are properly aired (and that is not the “Max Cold Inflation Pressure” listed on the side of the tire.
‘91 Ultrastar Champion‘02 Georgie Boy Landau 8.1l Workhorse
‘03 Jeep Wrangler TJ 2018 Jeep Wrangler JK toad