Don't let them push you into something you don't want.
And if you do want it - which we tend to at 37 weeks because we're sick of being pregnant - have a serious think about it and what the ramifications for your birth experience or your babies' health could be. In the end an extra few weeks of pregnancy isn't 'that' bad.

My Mid thought I was having a 10lb baby and DS was 8lb. That was from fundal and from looking at how I carried.
As for ultrasounds, IIRC they measure weight from the length of the femur - Do you think if someone measured your femur that would accurately gauge your weight? Just be careful with your options...

Before you let them dictate what your labour will be like because a guess of the size of your child, do some research about induction, early or otherwise. Many GD and PE labours that are induced at 37 wks end in CS because baby is not ready.

In the end it's your decision when it is offered... don't let them take that from you, you do have a right to say no. A 'big' baby is not going to be seriously damaging to your health if you go to 42 weeks.

Good luck with impending labour, I hope it is ultimately a safe delivery of your baby.