unit of weight is...
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The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, and about one-sixth as much on the Moon.
SI unit: newton (N)
Other units: pound-force (lbf)
In SI base units: kg⋅m⋅s−2