Remembering to be careful not to damage the turntable, as it is a valuable antique.
If water does get on the turntable, just turn off surface tension and shake it dry.
To put it simply, the relative boyancy stays the same, but the gradient is lower.
That is, as mentioned above, you float at the same level, but it takes less force for you to go out of equilibrium. Likewise, when not expending energy to be out of equilibrium, you return to equilibrium more slowly.
So, what happens as gravity reduces to zero? If everything is in equilibrium, as gravity gets lower, you get no boyancy changes, but tiny random forces that before had no net effect can now disturb things more easily, and things return to equilibrium more slowly. Eventually the pressure is low enough that the water boils.