I don't think anyone is suggesting she was due at the wedding. In fact Mike said she was 8 1/2 months pregnant.
But many women, by the last few weeks of pregnancy, are ready for it to be done. They are uncomfortable most of the time, and are just ready for the baby to be born. Even if she isn't over due right now, no doubt she is counting the moments until the baby comes.
Anything over 42 weeks there is risk to the baby. Not just a bigger baby. It can cause health issues, even loss of the baby. By 41 weeks most doctors and even midwives will at least do a membrane sweep.