Ted - I think the issue with a "heavy trailer" is actually a "too heavy" trailer for the tow vehicle, or a mis-loaded trailer (too much weight forward or rearward).
A trailer that's too heavy for the TV will overload the rear of the TV, causing a reduction in loading the front wheels, reducing steering stability (it also alters the caster angle, making the TV steer more "slowly").
Just as important, the over-weight trailer will have excessive positive caster, making the trailer more stable (in that it will resist steering inputs from the TV more).
Also, that excess weight will push on the TV more than it's suspension was designed for - causing the TV to be less stable.
One more thing - an overweight trailer can transition (itself and the tow vehicle) from a over-loaded hitch to an underloaded hitch during acceleration/braking. This can cause serious instability in the TV.
Try to picture the trailer as a mass with a pivot point (both vertical and lateral) at the axle. The tongue is the end of a lever that attaches to the TV.
There's a website that had a great technical breakdown of how it all works...if I can find it again I'll post.
Disclaimer: This is my amateur attempt at an explanation of a somewhat complex system of masses, inertia and moments. I'm sure there are others who have a more accurate description (or correct my errors).