Big baby

So I am due the 4th and they are inducing me that day if baby doesn't come before then (doesn't look like she will). The main reason is because my doctor is worried about her being too big. She has consistently measured 2-3 weeks ahead at every appointment since 34weeks (he measures with a tape measure, I haven't had an ultrasound since 20 weeks). Does anyone have any experience with this? Was the tape measuring accurate? Was your baby super large? My first was only 7lbs 14oz so I am super worried.