Wind is the problem. That low construction trailers of the same weight but virtually no sail area are not a decent comparison. The sway problem is exacerbated by different weights on each TT tire, not just each axle.
A square box trailer has winds piling up against the side, a loading that increases for every foot of length. Add to that the terrible exit (squared back) plus short wheel travel leaf sprung suspension lacking any sophistication and one has the worst possible configuration of trailer. Raised COG for slides makes bad worse again.
Weight isn't the problem, but man-made and natural winds. Put the rig on a long, sharp descent where hitch tension is minimized and expect the worst.
As a turbodiesel drivetrain will always be superior in fuel burn, so too will a truly aerodynamic travel trailer with independent suspension (with better roll center height) superior in wind-handling versus a box. The winds flow over (where ground clearance is lower) and pull at the trailer versus push it. A lesser effect.
The better the vehicles at the outset -- their design -- the less problematic are road hazards such as winds. And the one least talked about: tripping hazards.