Mass is entirely a property of the object. So the conditions and environment surrounding the object have no effect on it, and it doesn't change.
Weight is a measurement of the interaction between the object and its environment, so its weight changes as it moves from place to place.
Example:
A standard brass cylinder in a laboratory set of calibrated masses is marked "1 kilogram".
When you weigh it on Earth, the scale says "9.8 Newtons" or "2.2 pounds".
If you take the set of calibrated masses to the Moon with you, and weigh the same "1 kilogram" piece, it weighs "1.62 Newtons" or "5.8 ounces" up there.