Classical physics : Yes
Quantum physics : No
Mass is the matter contained throughout, in a body,
Matter is anything that has a mass, volume and can take any specific shape.
Obviously, you can gain or loose matter from an object but then only, the weight will change. For mass to change the body must move at the speed of light. ( E=mc^2)
Weight is the force by which a matter is pulled towards another matter but mass of these two matters is simply, the content of matter present inside each of these two matters, which generally remains constant, unless they are moving at the speed of light!