Understanding relationship between scale and position

Hi please help me understand something very fundamental.

This is a bit tricky to explain, but here I go:

If I have an empty game object and add two cubes as children initially at their default 1x1x1 unit scale size and position them at 0,0,0, but then I scale cube b in the y-axis to 3.0, then to position cube B so it's bottom face position matches the bottom face of cube B, I have to add cube B's localScale.y/2 minus cube A's local y-scale / 2 to it's current y position. This makes sense to me.

The thing I don't understand is if I add 2 additional empty game objects under the main parent one, and then add one cube to each of the intermediate gameobjects, and then scale the cube (which is now 2nd child, under 2 empty objects), to say 0.3, 0.3, 0.3, then when I try to position the middle child objects, the positioning gets magnified, i.e if I move it up the y-axis one unit, it actually appears to move 3! Multiplying the position by the scale of the cube (0.3) sorts it. I don't understand why the scale of the child object affects the positioning of the parent object?

What would happen if I had multiple child objects of different scales? Please explain what I am missing!

Thanks Simon