Will my doctor take me off the depression medication if I tell them how much it increased my appetite?

Depends. This is a discussion between you and your doctor (who knows your medical history best) but there are many other alternatives to choose from. I can't see why your doctor wouldn't want to try something else to prevent weight gain, especially if it worries you.
It depends. On a number of variables, such as how long you have been on the medication, how successful it have been in alleviating your depression and whether there might be a better medication out there for you. Talk with your doctor and express all your concerns. We are here to work with you.
Depression and weigh. Some people are more sensitive to weight side effects than others. All antidepressants can cause weight gain. Even if a patient improves a lot but also gains weight importantly, med need be changed if you already have a healthy lifestyle (if not, it is your bad life style that make you gain weight, not the med). Treatment need be planned so not to cause additional health problems by alleviating one.