How much weight should I be gaining each month if I am already overweight?

Depends. If you are overweight then i would stress eating a largely plant based diet of unprocessed food. The majority of your diet should be fruits and vegetables and fish. You should exercise everyday for at least 45 minutes. Walking, prenatal yoga, etc are examples. If you eat right and exercise, you may not put on any weight or even lose some initially.
Non. If your already overweight, you may need to lose weight unless you are very muscular or body building. Losing weight is not easy because behavior modification requires individualised approach. However exercise, reduced carbohydrates, meat, nuts and vegetables eating in small frequent meals works for most dedicated person.