In a coordinated level turn the aircraft is yawing, under the influence of the rudder, and pitching, under the influence of the elevator.
In a climbing or descending turn the aircraft is also rolling (in a climbing turn, opposite the turn direction, in a descending turn, with the turn direction), under the influence of the ailerons and the different angle of the attack on the wings.
"Weathercocking" is an undefined, colloquial term which only really applies to questions of stability. In any case, it doesn't apply in coordinated turning.