If my physics sources are correct (I'm including a non-technical one below), trailer sway is a function of weight distribution, speed, and tow vehicle/trailer weight ratio. Other factors play in, of course, but those seem to be the big three ...
Basically, any time the center of mass is behind the rear axle, the trailer sway may lead to unbalanced "fishtailing" where the swaying gets progressively worse. This won't necessarily happen at any speed, however. The below article argues that, for a given trailer/tow vehicle combo, there's a speed threshold. Once you go too fast, you run the risk of catastrophe. Looks like towing below 60 mph and using trailer brakes or a trailer sway control hitch will help with unbalanced trailers.
I'm going to have to look into this more. Really important stuff.
http://oppositelock.kinja.com/tow-me-down-1609112611