Newton is the SI unit of force. newton is not used to measure weight. weight is the amount of gravity which pulls us toward the ground. In moon the gravity is only 1/6 of the earth's gravity.so if a man is 60kg on earth he is only 10kg in moon. I think you understanding what I am talking about.
AND DO NOT GET CONFUSED WITH THE DIFFERENCE OF FORCE AND WEIGHT
ANOTHER UNIT OF FORCE ,CALLED GRAVITATIONAL ITS UNIT IS KILOGRAM FORCE ( SYMBOL IS kgf )