We pulled our 16'
Scamp for one season and experienced similar bouncing. The
tires were new and we paid to have the frame and
axle inspected before we took our trailer out for our first trip. All checked out fine but we still bounced around more than I would have preferred.
While at the service center, it was suggested that most of our problem was being caused by incorrect hitch height. The trailer was riding behind the tow vehicle at a slight angle and this enhanced the squirreliness of the trailer towing. We added a 6" drop hitch to our receiver and this helped immediately.
The other point that was suggested on this forum was that we needed to put our camping gear in the trailer to
weight it down, since we'd been pulling it around empty. The
Scamp only weighs about 2,000 pounds dry
weight, depending on year and floor plan.
Ultimately, we decided that we simply didn't want to pull our camper any faster than about 60 mph and that 55 mph was the sweet spot for best handling. Faster than 60 mph and it didn't take much to allow the trailer to jump into the air over bumps. Of course, your experiences may differ...