Weight in the bed probably would have helped. Putting more weight on the tongue would help too (shift the location of the tractor on the trailer).

The rear springs are really soft in the first place and tend to have a lot of axle wrap, so that combined with not enough weight on them probably gave you the rubber band effect due to the rear springs wrapping up. Worn shocks would make the problem seem worse too.

I've hauled loads up to 5K or more, but nearly half that is in the bed, and it handled fine.
I hauled a trailer full of concrete one other time and they set it up w/ no load on the tongue. When I came to a stop on a downhill turn, the trailer tried to push the rear of the truck around (jack knife) and it handled really crappy. The hitch was adjustable, so I stopped and cranked it lower to put more weight on the tongue and it was much better.

Towing with my 4runner, if I don't have enough tongue weight, the rig and trailer will oscillate and sway really badly (especially if the 4runner is empty) even with relatively small loads, so I have to stop and redistribute the weight in the trailer and then all is well.

Seems like its a learning process...