Verified answer

assuming there is a pressurized dome to do the experiment

I am not sure but remember BOTH the gravity on the water and object is reduced

I think the effects cancel and the float level is the same

imagine a HIgh g planet, would the object sink?

interesting Q.

g Moon 1/6 g earth. Weight = mg for both water and object weight density of both are reduced

mass stays the same

the water object system would not "know here they are" unless g = 0

It will float higher, as the gravity pulls it at only 1/6 of earths gravity. Even the pressure of any liquid will be less than on earth, so the buyancy of the floating object will be less.

Lower gravitational pull on both water and object would cause increase space between atom's in both, therefore each more expanded,yet in the same proportion making object float same level but higher from surface of the moon.

It will float at higher level because the gravitaion force on moon is 1/6 th that of earth. The body will be lighter there.