I supose in the olden days, weight may have been an indication of how healthy the baby was likely to be, or it's chance of survival? These days, people just ask so they can think "Wow, what a biffer" and "Bleedin' hell, she's gonna be left with a fanny like a stitched-up channel tunnel".
Plaid Cymri tells me he was 10lbs 10ozs when he was born. The visiting doctor, who was a Scot, took one look at him and said "Tosh - what a whopper he is Mary". I think he meant "Fat Welsh F****r".