Your first response has it right. Weight is determined by gravity. To understand this better, it’s helpful to think of mass as the “stuff” that an object is made of. All of it’s atoms. All of them. This amount doesn’t change whether you’re on earth or the moon, for example. You are you in both places. Your weight however, changes from earth to the moon, because the gravity, or force that pulls you and the earth together, is different from the gravity of the moon. The earth and you are attracted more strongly and you therefore have a greater weight. If you were on Jupiter you’d weigh even more than you do on earth. Much, much more.