Having followed a number of trailers I noticed a lot of swaying on some, and have heard that towing a 5th wheel eliminates that sway. I have been looking at short 5th wheels and trailers in the 20-25 ...
A trailer needs around 10% - 15% of its weight to rest on the hitch. Too little results in sway. That's almost always the case with a shorter trailer. Sway can be induced by side wind too.
Many people intentionally wiggle the trailer to get a peek behind it. Before I got a rear view camera, I did that.