Lots of people have overdue babies that come in their own time. My biggest boofhead was 10 days overdue. Yet both my girls were a week early. You have to remember that a due date is only an 'estimate' and different babies need different amounts of time inside before they are ready to join the world.

As for your midwife going on about the placenta - she is partially correct. There can be some slight increased risks, but those aren't usually until at least 42weeks pregnant. And not everyone has issues (in fact most women won't). I've know women to go three and four weeks over their edd with no placenta issues at all. And some women have placenta issues eleven though they've gone 'early'.