This maneuver is called weather cocking and it is caused by aerodynamic forces on the rocket. The weather vane acts like an airplane rudder, pivoting about the vertical bar and always points into the wind. Older, more artistic weather vanes used the figure of a rooster with large flaring tail feathers instead of the wing shown on the figure. This type of weather vane was called a weather cock. As the rocket accelerates away from the launch pad, the velocity increases and the aerodynamic forces on the rocket increase.
Aerodynamic forces depend on the square of the velocity of the air passing the vehicle.
If no wind were present, the flight path would be vertical as shown at the left of the figure, and the relative air velocity would also be vertical and in a direction opposite to the flight path. If you were on the rocket, the air would appear to move past you toward the rear of the rocket. Regardless of wind direction, the wind introduces an additional velocity component perpendicular to the flight path. The addition of this component produces an effective flow direction at an angle to the flight path that depends on the relative magnitude of the wind and the rocket velocity. Since the effective flow is inclined to the rocket axis, an aerodynamic lift force is generated by the rocket body and fins.