Why do they think she's going to have a big baby?
So far as I know, the risk increases after 42 weeks (although there is some differing info on this). The line in the sand seems to be a bit arbitrary though, as some doctors/hospitals seem to insist on 40, 41, 41+3 or 42 weeks as a cutoff, while some (particularly midwifery-led practices) will also suggest it's safe to continue gestating (if the mother wishes) with regular monitoring after 42 weeks.
There is research concluding that routine induction at 41 weeks did not improve outcomes.