I'm in a profession that scares people sometimes, and I often say the same thing to people who admit to being nervous, though sometimes I ask them what it is that's making them nervous to see if there's something I can do to make them more comfortable. But being on the other side of that, the best way I alleviate fears is to move forward and let them experience me as not all that scary as we work together, and as they see I keep my word and good things come of working with me. Sometimes trying too hard to reassure people can just make things worse.
But I empathize as well, as I'm terrified of all medical personnel of any stripe. You're brave for doing what you're doing. I'm so glad that you seem to be getting along well so far.

I hope you'll work well together.
As for the birth related questions, low birth weight can be a predictor of certain issues later in life.