If you stand on a pair of bathroom scales, explain how the readings change as yo

Your center of mass (COM) probably being between your feet and somewhere up near the belly the momentum to keep you from falling (i.e. rotating around that center) to one or the other side comes from the forces the respective scales exert on your feet multiplied by the respective levers to your COM. Both levers being of the same length (i.e. you standing just above and between the scales you will have two identical forces and half your weight shown on each scale.

The scales being sufficiently horizontally positioned on the floor at a distance L+R (distance from left / right scale to COM and nearly identical to the levers to your COM if your legs are vertical to floor) you will see that the forces/weights shift around 50% each depending on the linear ratio of L versus R. I assume greater ratios produce more error due to genuflection and such.

I hope that was neither too theoretical nor too wordy.

The sum of the weights on the scale equals the total weight.