Just moving your jaw up and down is not going to cause your face to lose weight. As you lose weight all over your body you will lose weight in your face. And it depends on the person. As I lose weight my face really loses its fullness. You have fat in your face just as you do on the rest of your body and the only way to lose it through diet and exercise.

Amusing, excessive consumption of gum may cause laxative effects. So I guess weight loss could occur :d