Large gestational age

Has anyone else had their doc tell them the baby is large? I’m 35 weeks, 5 days and my belly is measuring 36 weeks (2 days, for real??) and they scheduled an ultrasound for next week to see if he’s really large. Then they said they would have to schedule a c section, and wouldn’t induce until 39 weeks. It all seems so counter intuitive to me. Like, why wouldn’t they induce at 37 or 38 if he’s big so he doesn’t get bigger, rather than schedule a c section for a second baby, who might not actually be that large. I’d love to hear from anyone else who has experienced this! What did you do??