I have a Grado Reference cartridge mounted in a Rega RB900 arm, mounted on a VPI HW-19 Mk 4 turntable (hardly a light TT). I also have occasional problems with the Grado "wobble". The floors in my house are wood, suspended above a 3-foot crawl space, and with recorded material that has lots of deep bass (such as pedal organ), the problem can be acute. I've come to the conclusion that my Grado, and maybe yours, is vulnerable to acoustic feedback.
I suspect that your problem is due to the light turntable AND the floors. A good turntable isolation base might help (such as the Bright Star Big Rock), but if your setup allows you to wall mount a turntable shelf, that might be your best bet. The other precautionary step you should take is to make sure the tonearm cable is well isolated and not feeding acoustic vibrations back up into the tonearm. I wrapped the phono cables (leading from the Rega arm to the phono preamp) in bubble pack material, so the cables don't directly touch the audio cabinet surfaces. These sorts of problems can be aggravating, so try a number of approaches to improve the isolation of your turntable.
I suspect that your problem is due to the light turntable AND the floors. A good turntable isolation base might help (such as the Bright Star Big Rock), but if your setup allows you to wall mount a turntable shelf, that might be your best bet. The other precautionary step you should take is to make sure the tonearm cable is well isolated and not feeding acoustic vibrations back up into the tonearm. I wrapped the phono cables (leading from the Rega arm to the phono preamp) in bubble pack material, so the cables don't directly touch the audio cabinet surfaces. These sorts of problems can be aggravating, so try a number of approaches to improve the isolation of your turntable.