for some reason, when I change density to 0 on an object, it still falls....is that supposed to happen?
Yes, the object is given "mass" by it's size. Density will not take away mass.
To make the object immovable, set it to immovable in physics-proporties.
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What if I just want it to be weightless?
If you want it to be weightless, just turn off the world gravity, add the OTHER (non-weightless) objects to a family, and apply a constant downwards force to those objects.