This is a misleading oversimplifiation.

First, there is no independent thing as head weight if you have good posture. The head is merely an extension of your spine - "head weight" is merely a carefull use of sway to initiate the next action. We only call it head weight because the head plays a greater role than the upper body, but the upper body must stay in position relative to the head - no dumping you head to the side on it's own.

Second, be very carefull not to confuse the direction in which the head is looking, with the position of the head and upper body weight relative to the pressure center in the standing foot - they are not the same.

You can have your head weight encouraing movement in one direction, be looking in another, and still be maintaing the leftward stretch of you head relative to your body, all at the same time without conflict.