Counter intuitive perhaps, but try disconnecting the ground wire. Next make sure your 'wires' are not routed near any power supplies or transformers.
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There's lots of different sources of hum but the clue here is it starts when the volume is turned up and gets worse until turned down again. This one thing is all we need to know it is a feedback problem. Playing music excites everything in the room, including the turntable, which being what it is amplifies the feedback and just like a microphone feedback it gets louder and louder.
Had this same problem myself one time so I know.
Eliminating this problem is as simple as breaking the feedback cycle. This could be anything from as easy as putting the turntable on something massive like a sand bed, to putting it on springs (Nobsound are cheap and effective) to leaving the turntable alone and putting the speakers on springs.
Or if you are smart, putting everything on springs. Or if you are really smart and want to not only eliminate your problem but give your whole system a mega upgrade, then put the turntable on Townshend Pods.
Seriously, springs are the answer. Do a search for Nobsound, for how little they cost ($30!) they are insanely good. Find the thread where everyone gushes about how great they work. Or if you can afford it and want the very best, Townshend Pods will show you just how far you can go with something as seemingly simple as a spring.