Single axle might be part of the problem.
Traveling at 65 mph might be a factor as well.
Do you have an Anti-Sway Bar? This might help keep the sway away & help bring it back under control. I you have one, perhaps tighten down a little more might also help.
Having a heavy TV compared to the trailer, shouldn't be a cause & should keep the tail from wagging the dog.
If you have breaks on the trailer, one can use them to manually apply them to the trailer (without breaking the tow) which should help strengthen the trailer.
Make sure you do not have much weight in the rear of the trailer. This makes them easy to sway.
At least the above things have work for or against me towing the Scamp.