I reckon the race weight guides are bollocks. They give me a BMI of 17ish. I've been that light, and was bonking walking 100yrds to the letter box. I certainly wasn't running!
I know nothing about achilles problems, but would always advise consulting a physio/sports medicine bod rather than your GP. Standard GP advice for any running injury is stop running. Unhelpful, although less dangerous than advising starving yourself til you break down.
(5'5" and 56kg. Ultra runner, although quite how I get my vast weight up the hills I have no idea. And there's millionaires shortbread in the kitchen.)