The phenomon is fairly common if you happen to look - so few of us seem to look at the night sky these days or are even able to see it for light pollution from cities.

I wonder about the association with bad weather. Weather folklore is usually based on observation rather than superstition. Bad weather in the British Isles usually comes from the west, and a New Moon is in the western sky. If there were a large amount of cloud cover to the west, bringing bad weather with it, this might increase the earth's reflectivity and the amount of earthlight reaching the surface of the moon. The 'old moon in the new moon's arms' would become more visible than usual. Just an idea.