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While I believe that trying to achieve a uniform definition of weight in this world is truly tilting a windmill, I can't help getting involved. To my way of thinking, the only useful definition of weight is that which the bathroom scale reads when you stand on it (assuming it is an accurate bathroom scale). This is not inconsistent with Al Bartlett's definition, only a little homier.
True weight is mg, while apparent weight is given by a bathroom scale,
which shows the upward support force. Jump off a cliff, and that scale
reads zero. You have no apparent weight, just like those floating
astronauts in the orbiting shuttle. Plenty of true weight. You can also
hang a wood block with a spring scale. Release the block and it falls due
to its true weight. But the scale reads zero while the block falls.