Can you borrow a stethoscope? Put it on the base and listen, then put the stethoscope head on whatever the turntable is resting on and compare. If you hear a lot of sound when it's on the turntable, press a finger in the turntable base- just doing that will suppress a lot of the energy. Also, tap on whatever the turntable is resting on- if you hear a lot of sound, go to a Rockler Woodworking store and buy a set of 'bench cookies'. People use them to isolate turntables, as well as their intended uses.
How loudly do you listen to music? If it's not terribly loud, I'm not sure I would obsess about this unless the bass response from your speakers is extremely strong and the turntable is in a place where the energy is strongest.
I had a JVC turntable that would produce feedback as soon as the level reached what I would call 'loud', but it wasn't very heavy, either. The base was made of particle board and I didn't have it for long. The table I have now is much heavier, the base is heavy resin plastic and if I tap on the base, it's audible, but I haven't had issues from that.