Weekly doctor visit

Chelsie • Married: 04-12-2015. Due date: 06/28/16. Currently pursuing a Master`s degree in Secondary Education (6-12 grade).
Went for my weekly checkup. I'm currently 37+3. He said baby is a "good size" and if she gets too much bigger then a c section would be possible. I'm wondering how big is too big?? And does that mean she should be coming soon cause she's big? My cervix is still closed but baby is all the way engaged and he could feel the head pressing on the cervix.