I bothered to look at a crane fly through a magnifying glass for the first time this morning. I noticed two stalks coming out of the body with a blob at the end, one on each side, a bit like dumbbells. It occurred to me that these could be to do with stabilisation in flight.
It turns out that they are called halteres. They are actually sensors that give information about rotation in flight. The article compares them to gyroscopes and says that the Coriolis Effect comes into play. I'll need to consider how that actually works here.