Trailers sway because they are not setup properly. You can fix the setup (sometimes just not possible if a poor design) or you can change the way you tow it (use Hensley or Propride)and hope for best.
Proper inflation of all tires (both trailer and tow vehicle,
Proper weight balance on trailer,
Within weight capability of truck,
proper attitude of trailer (does it sit level when hooked up and ready to go?)
I am not an expert nor claim to be, but I have done my research and enjoy pleasant towing without sway and without hensley or propride hitch.
I have experienced sway many years ago when I did not have a car trailer properly loaded (and over loaded) behind my S10 blazer. There was a bump in the freeway on a curve that started the sway and it tossed that S10 Blazer back and forth across 3 lanes of freeway, cars got out of the way fast... I just wanted to stop and without knowing better, jumped on the brakes when the trailer was in line with the S10... It stopped the sway immediately when the surge brakes on the trailer came on.. we were very fortunate not to get injured or get others injured. Since then I make sure I am properly loaded (right amount of tongue weight, right attitude of trailer, etc)... YMMV
Also note, I would not turn down a good price on a Propride hitch even though I tow without sway (updated design of Hensley by the inventor himself).