What is the amount of "stuff in an object?

Good question. The amount of 'stuff' in an object is it's mass. 

A fundamental distinction we learn in physics is the difference between mass and weight. If we were in deep space, away from any very large objects of mass (like a planet), we would be 'weightless' e.g. not feel the effects of gravity, but we would not be 'massless'. Our mass doesn't change based upon our proximity to large objects (gravitational attraction), but the sense of weight does.