Archimedes' Principle states that a body in a fluid experiences a buoyancy force equal to the weight of the fluid it displaces.
In this case, the weight of the fluid will be the gravitational attraction it feels due to everything else present, i.e. the rest of the fluid and the heavy mass. It doesn't matter if you consider the gravitational attraction it feels due to itself, because it will cancel out.
Note that the gravitational attraction of the rest of the fluid is not affected by the presence or absence of that displaced fluid part. The net gravitational field will be affected, though. But we do not need to consider that.
So all you need to do is compute the gravitational attraction the displaced fluid would feel, and that will be equal to the buoyancy force on the mass-less object.