If it were me, I would decline these routine exams.
Often, providers will strip your membranes during these routine vaginal exams in the last month of pregnancy, without even telling you. Stripping membranes can start labor (not always, though). However, with any vaginal exam, there is a risk of infection.
There is no real reason for your OB to be doing these weekly exams, except to 1. be monitoring your cervix for 'ripeness' to determine if you are favorable to induction
: or 2. to be stripping your membranes to get labor started.
Knowing how dilated or effaced you are right now (or even in labor, for that matter) is pretty much meaningless. It isn't uncommon for women to either walk around for weeks at 4-5 cms. dilation or have a totally undilated cervix and have their baby the very next day.