Its formula, W=m x g,
is similar with that of force, F=m x a;
but what you should note is that acceleration was replaced by a constant or uniform acceleration, g which is equal to 9.81m/s2.
Hence, the SI unit of weight is the Newtons, N.
But mass is a constant as long as classical physics is concerned. Its a measure of the stuff contained in a matter. The SI unit is in kilograms, kg.
hence the weight of a substance is constant at a place but varies with change in gravitational pull.
This means that a man in a moon will weigh less than someone on earth.
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