O and my son weighed 5.15 at birth so he was on the small side too.
With my son at 37 weeks my membranes were swept to try and induce me BC it wasn't doing him any good to stay put since I lost 5lbs that week due to GD and gallbladder issue. She said if it didn't work then she was inducing me the next week. Luckily he decided he was ready 3 days later so didn't have to induce.
I'm not sure. But if baby is small you'd think they'd wanna keep her in the oven longer lol