Thanks everyone who responded. My lovely little girl was born on Friday 11th April weighing 2.93kg (6lb 7oz), so the sonographer was just about spot on. Thankfully she's perfectly healthy, just small. I asked the ob about my placenta (birth was an emergency caesar) and apparently it looked fine. I wish I hadn't known about the size; it made the last few days of my pregnancy very stressful anxious ones. I was in tears during the op because I was so worried about the baby - luckily it was over quickly and I was SO relieved to find out she was OK.

In case anyone out there has the same worry, I can confirm that it is DEFINITELY possible to have a healthy second child who weighs much less than the first!