The object has a mass of 120 kg everywhere.
-- It weighs about 1,176 Newtons (264.6 pounds) when it's on the Earth.
-- It weighs about 195 Newtons (43.8 pounds) when it's on the moon.
-- When it's in a space-ship coasting from the Earth to the Moon, it still
has 120 kg of mass, but when you try to weigh it, it floats off of the scale.