Some possible solutions.--Would check my tow vehicle tires and bearings.Had 2000 model Chevy pulling boat that did same thing.Found a bad right front wheel bearing assembly,fixed it,stopped the trailer vibration.Can't explain it,but it fixed problem.Might check trailer bearings also.Have seen bent trailer axle cause vibration,but mostly on an empty trailer.Also remove rims from trailer and check for dirt or rust buildup on hub face.If rim doesn't mate flush with hub can cause problem.Good way to check for good fit between rim and hub is to burn a sooty rag around hub,thoroughly covering hub with soot,put rim on,torque to factory specs and then remove .Look for a good rim pattern on hub.Another possibility (remote at best) is a caliper or brakeshoe dragging a little ,causing a little tire hop.Also jack up trailer, 1 tire at time,then get a good solid object next to tire,take a straight edge and hold close to edge of trailer rim and spin rim to check if rim is running true.Would detect a warped rim.
Quick way to eliminate your tow vehicle as a cause would be to get a buddy to pull trailer and see if it still vibrates at same speed.