Big baby?

I had a scan at 32 weeks and was told baby is estimated right now at 5lbs 7oz. My consultant said it may just be a growth spurt and babys weight gain might slow down so I will be scanned again at 37ish weeks. I want to try and avoid a section. Was any other mums told they would have a big baby and still gave birth vaginally. Slightly worried. My daughter was 5lbs 15oz at birth born at 38 weeks.