I'm confused about how gravity affects objects with an irregular center of gravity.

The essential question is, does a weighted die still work under a vacuum? On the one hand, one side of the die has a greater gravitational force that should cause it to rotate until the heavy side is closer to the ground and this should hypothetically occur regardless of air resistance.

On the other hand, the gravitational acceleration is constant for the entire die regardless of mass, so removing air resistance and an initial dropping angle parallel to the ground should create a weighted die that doesn't work? Someone clarify my poor understanding please.

Edit: Getting different answers here still... Still confused