First: Put the sewing machine on a different table and use it. Does it still vibrate like crazy? If so, the machine is probably the culprit.
Second: Have you ever gone into a restaurant and been seated at a table that rocks? It sounds like you could have a similar problem.
Maybe you could put shims under the legs until the vibration either stops or is minimized. It's trial and error, no doubt. I was thinking you might be able to do it with those little pads of paper with sticky glue on one end. Set a full pad under each of the legs, then take off a few of the papers at a time from each leg until the table is not vibrating so much.
Mind you, I have not tried this method, but it's pretty cheap to try. If it works, you have the levels needed for each leg and can use the pads to find a more durable shim.
Last edited by cathyvv; 10-22-2018 at 08:24 AM.