A flap that covers an entrance or forms a rooflike
extension for a tent or the canopy of a vehicle

Hmmm, I'd always thought a "flysheet" was so-named because it kept of flies . Which wouldn't be a very healthy association in the current context.

Now I can see that what most of the pertinent definitions have in common is that one bit of material/cloth lies (or flies) over other bits of material/cloth.

So thank you, I've learned something today