Chewing gum works your muscles inside your mouth and jaw muscles so chewing gum does burn a few calories but it doesn't burn a lot of calories.
You won't lose much weight chewing gum although you will burn at least a few calories.
If you want to burn off calories too lose enough weight you need to exercise by running, walking, jogging etc or use a treadmill, exercise bike or even a rowing machine.
You also need to watch your calorie intake when trying to lose weight.