Fill a balloon with Helium and it floats (it is buoyant in air). 'Fill' a balloon with a vacuum (not withstanding the difficulty of a structurally stable void) and it is more buoyant as it is less dense. If you filled a balloon with a theoretical 'anti-helium' (not withstanding annihilation) - would it be more or less dense than the vacuum. Would it 'float' as per posi-helium, sink or would it be twice as buoyant, relatively.
Antimatter is experimentally known to have positive energy density and positive inertial mass. Antimatter responds to electromagnetic fields exactly as we would expect a particle of their mass and charge to respond.
We expect that antimatter also responds to gravity exactly as we would expect a particle of their mass to respond. In other words, we expect antimatter to fall down, not up and we expect a large clump of antimatter to gravitationally attract both matter and other antimatter. However, to date that has not been experimentally confirmed due to the weakness of gravity.
The question is based on a false premise: that the buoyant force on an object depends on the density of the object
In fact, the buoyant force on an object depends only on the volume of the object, the density of the medium, and the local acceleration of gravity. A cubic metre container submerged in water experiences a buoyant force of $9,800$ Newtons, irrespective of whether it is filled with vacuum, hydrogen, helium, air, iron, lead, or osmium (densest element, $22.9$ g/cc).
The density of the submerged object only becomes important if one wishes to know the net result of the combined forces of gravity and buoyancy on the object. The answer of @Dale deals with this question in regard to antimatter.