You're banked in a turn, the plane is constantly in a "new" slip because it's always under acceleration if it's in a turn. Weathercocking effect is always in present and that's why you are coordinated and turning. The forces that caused the initial slip didn't go away, they just have a new vector.
If you enter into a turn properly, there won't be any slip during entry or during the turn. If your ball is centered then you are coordinated. That's why there is an instrument called the "turn and slip indicator".
The rudder is the force that is making the tail "come around" and point the nose in the turn. it's creating a cambered surface and is essentially a wing standing on end. So as the rudder deflects
left, it creates camber and lift which acts 90 degrees perpendicular to the surface, ie: to the
right! This then rotates the airplane around the CofG to point the nose into the turn. It's exactly the same as applying elevator to adjust the pitch of the aircraft!! This isn't weathercocking! If it was, then the wing would fly because it's "weathercocking" which isn't true.
"Weathercocking" is an undefined, colloquial term which only really applies to questions of stability. In any case, it doesn't apply in coordinated turning.
Yes yes yes!! the key word is "stability".
I thought "weather cocking" was the term used to explain why the aircraft wants to turn into wind whilst on the runway when it experiences a cross wind.
That is correct. In that case it acts like a weathervane. While in flight it doesn't matter where the wind is, only the direction of the relative airflow.