less electrons in the valence orbital cloud means that the effect of the nucleus has less effect on them. for example, potassium has 1 valent electron, so the effect of the nucleus on this electron cant help the elctron more than the other 18 electrons its looking after, so this poor little guy out in the valent orbital is effected less by the positive effect of the nucleus.
take this explanation, reverse it and it explains why the radii is smaller for right side.