Incorrect.if i am not wrong, the center-weighted is not remains in the center of the frame but follows your focus point if you are using single point focusing mode.
Actually all the information on center weighted metering posted is incorrect.
Center weighted metering has an inner circle and an external region. BOTH are metered but 70-80% of the evaluation by the light meter is performed on the inner circle. The exact diameter of the circle varies from camera to camera as does the amount of weighting applied.
Some cameras such as Nikons Professional series F5, F6, D2, D3 series have adjustable diameter center circles.