I recently bought a 6x10 utility trailer. We used it to move my son into his new home. The first load we put some light stuff in the fron t and the washer and dryer in the back. All was well until we hit about 50 mph. That little trailer swayed so hard that it actually rocked the truck side to side....
I pulled over, unloaded and reloaded the trailer with the heavy stuff up front, and had no problem driving 70+ mph....
Could be as simple as not enough weight in the front of your small trailer causing swaying and causing your TT to sway also. Does the TT sway without the small trailer attached??