Induction due to baby's size?

AC

Since my 20 week anatomy scan, our little guy has been measuring just over a week ahead. My midwife wants to induce me at 39 weeks because of this. I am currently 37+4. At 36+1, I had a cervical check and was not dilated or effaced. At my 37 week appointment, he was not engaged either. My question is, should I go ahead and be induced at 39 weeks, or fight it a little more?