Do trailers with coil springs and shock absorbers sway at higher speeds?

My Avionic trailer has leaf springs and no shocks and the rhythmic ass end sway that develops at higher speeds encourages me to keep the top speed at 60-65 mph. That speed is just fine with me except when interstate traffic if flying by at 80 mph. In that case I feel that I'm something of a hazard, especially if I'm trying to merge or change lanes.

I'm thinking that shocks might dampen out the rhythmic sway that seems to be self-reinforcing. Tow vehicle is 2004 Volvo XC70. Single seat glass glider.