Induction question

I'm currently 37w 2d and last Tues I had a growth scan done and my baby weighed 5lb 1oz. I'll be going to appts every week now. My Dr said that she doesn't want baby going over 6lbs (I'm only 5ft and want to do vaginal delivery) and said I won't go past my due date. I've heard babies grow the most in the last couple of weeks. Do you ladies think she will end up inducing me soon?