What's wrong with big babies? They really aren't any more difficult to birth than small babies. The weight babies gain in the last few days is fat...and fat squishes. You aren't technically "late" until 42 weeks. I suspect you are only 40 weeks and 4 days. Not late at all. 40 weeks is only an average. As long as everything is healthy inside for baby, it's better to let baby come out on their own time. You really can just say "no" to unnecessary induction.
That said, I know how difficult it is to say no to over-ambitious OBs. Keep doing what you're doing...and maybe cancel that appointment and reschedule for Thursday or Friday. They can't bully you if you aren't there.