As others have replied, there are many things that will help. None will get rid of all the wiggle. The trailer is sitting on its suspension and tires. Only way to get all the wiggle, is put the trailer up on blocks.
I added stabilizers. Close to center of the trailer, one in front and one behind the axles. They need a very long crank handle, which I had manufactured at a welding shop.
I also, put blocks under the corner stabilizers (they work better, when not fully extended) and, after the trailer has settled for a couple hours, I snug the stabilizers again. Depending on weather (rain) and ground conditions, I may snug them daily.