Would they induce me?

Rahnny29

During our 40 week check-up yesterday, I measured at 41 weeks when I was technically 40 weeks 1 day. I'm only dilated 1 cm and 50% effaced, still carrying high. The dr. seemed concerned with baby's heart rate so she hooked us up to a fetal monitor. 30 min. later we were up in labor and delivery for more monitoring. The baseline of his heart rate was around 125, but they still sent us home after 40 min. in L & D. They scheduled an ultrasound for this morning because my doctor is concerned about how big he could be getting. 

 Everyone has been totally friendly, but my DH and I ate feeling a little uninformed. Should we be worried about any of this?  If the baby is really big, is there a chance I'll be induced? Part of me is rooting for it because I'm uncomfortable and want to meet him. But I also hope for a normal, healthy birth. Has anyone had a similar situation in the past?