Weight and mass are not the same -
Weight is a force measured in Newtons (N). Weight is caused by the pull of gravity.
Mass is not a force. It's just the amount of 'stuff' in an object. For any given object this will have the same value anywhere in the Universe. Mass is measured in Kilograms (Kg).
An object has the same mass whether it's on Earth or on the moon - but it's weight will be different.
On Earth, the strength of gravity is 10 N/kg
On the Moon, gravity is weaker so is only about 1.6 N/kg.
Falling obiects in a vacuum accelerate at the same rate