R., I am overweight and was when I had my baby almost a year ago. I didn't have gestational diabetes, either. My son weighed a whopping 10lb 15oz and was 22inches long at birth! I had to have a c-section because of his size as an ultrasound the day before my c-section guessed him to be 10lb 2oz (we was bigger!) and they were afraid I would deliver his head, but then have his belly get stuck and end up having an emergency c-section anyway.
My OB told me that his size had nothing to do with my size, though. Some babies are just big!
Inducing before 37 weeks is very risky as the baby needs time to develop their lungs. My son was born at 39 weeks as was that big. My OB wouldn't induce any earlier because of the lung issue. Just because a baby is big doesn't mean that their lungs are developed, so I would be very leary of inducing a month early.
I hope that helps!