Question

Two objects with the same weight and different volumes, may have different Masses, have different densities or both

Answer 1

If they had different masses, they would have different weights, so think about that and see if you can narrow this down. \[ \vec{F}_g = m\vec{g} \quad\text{so, }\quad \vec{F}_g \propto m\]
If the two objects are in the same place (so the gravitational force is the same), they will have the same weight if they have the same mass, regardless of volume or density, since weight varies ptoportionately to mass.