Heidegger describes two ways of assessing the weight of a hammer. On the one hand, we can put it on a scale and get a numerical read-out. It weighs three pounds. What it’s for doesn’t make any difference. It’s a generic object on which gravity exerts a particular force, which we can measure.
Alternatively, we can ask the carpenter, who might tell us that the hammer is “too light” or “too heavy.” This assessment depends on the use of the hammer. It is a human measure, having to do with work and social interaction, a measure that makes no sense in a mathematical/physical framework.
Which is the real weight of the hammer? Which assessment of weight should define the public meaning of “weight”? On the answer to these questions, a great deal turns.