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I think you've correctly analyzed what drives the discussion. Is it fair to say that you are using the "Bartlett" definition of weight, but with the proviso that one always choose the earth surface frame of reference? (I don't think you are equating weight with GMm/r^2, i.e. Newtonian gravitational force, or are you?)Correct--Weight = mg with g as measured by someone standing on 'earth'. However, if one goes to the moon, weight would involve the local free-fall acceleration as viewed from the moon's surface. I do have a project (for my gen-ed students) determining the performance in several Olympic events if the games were conducted in an air filled dome, on the moon.