All I could think about was a box of feathers would be a lot lighter than the same size box of rocks!
Don't confuse
density (mass/volume) with
weight or
mass. The old kids' question, "which weighs more, a ton of feathers or a ton of lead?" comes to mind.
As started above, mass is a property of the material. If you were in zero gravity, any mass would have zero weight. On the moon where gravity is less, you would weigh less than you do on earth -- but you'd have the same
mass.
We normally use
weight to determine mass -- at least here on earth. However, in very accurate experiments, we have to correct for small changes in the force of gravity (gravity is less at higher altitudes, for example) and for the
buoyancy of the material in air. The buoyancy requires a knowledge of the volume of the object.