Newton 

A newton is the SI (derived) unit for force (including weight). In terms of SI BaseUnits it is $m.kg.s^{2}$
Weight is commonly (and technically incorrectly) given in kilograms (kg). To convert a 'weight' (actually a mass) in kg to a force in newtons we can multiply by the Earth's acceleration due to gravity $~=9.8m/s^{2}.$
Of course, in a different location (say the moon), the mass (in kg) remains the same, but the weight (in newtons) will be different (acceleration due to gravity on the moon is roughly $1.63m/s^{2}$ ).