Weathervaning

Just a quick question...

During a crosswind landing, for instance a left crosswind, you'd lower
the left, upwind wing to counter the right drift induced by the
crosswind.

You'd also use some right rudder to keep the nose straight and prevent
it from "weathervaning".

Is this "weathervaning effect" caused by your leftward relative motion
due to the left bank OR by the rightward crosswind ITSELF?
Personally, I think that the former applies. The rightward crosswind
only displaces the airplane to the right. Only the relative motion of
the airplane with respect to that airmass would induce the
weathervaning effect. I presume that the airplane does not know,
aerodynamically, of the left crosswind.

Next thing I was wondering, which is related to the above: say you're
dead on centerline on landing, and all of a sudden a crosswind from
the left starts blowing. The effect would be that you should only be
displaced to the right of runway centerline. Your airplane nose would
still be parallel to the centerline. Do you agree?

Alex