All good advice above. Many people get used to the "shimmy" and do nothing. Others use bottle jacks or mount additional stab jacks in the middle. Others go with more significant stabilizers such as the JT's and others like them.
The issue seems to be worse the longer the trailer. I believe this is caused by the leaf springs and tires having some bounce in them and anything you can do to remove this will help most significantly once the corner stab jacks are firmly snugged. Also remember to recheck the corner stabs after 24 hours or so as some loosening does seem to occur for most people.
Good luck in solving but the info above from the others has all been reported to work for different folks.