How does headwind influence the results of a pitot tube and therefore the airspeed indicator?
The pitot-static system (and the airspeed indicator) doesn't care about the speed of the aircraft with respect to the ground. It is concerned only with the speed of air with respect to the aircraft (that is why it is called airspeed and not groundspeed indicator).

So, if your aircraft is on ground and experiences a headwind of 60 kt, the airspeed indicator will show an airspeed of 60 kt, in an ideal case.

This is important because the wing generates lift depending on the airspeed, not the ground speed (forgetting about stuff like ground effect, etc.). This means that if an aircraft is parked on the ground and there is a headwind of sufficient velocity, it will try to lift the aircraft up.