Jim, look at it this way. I weight about 180lbs.
Lets say I am exactly proportionate on my left and right sides.
Example, my wife gets mad, hits me on the head with an axe, and it splits me into 2 portions, left and right. Those 2 weight the same amount.
Now, lets say I was glued back together, and stand on a scale. If I lift my right arm straight out, perpendicular to my body, that is a cantilever of sorts.
Now, in doing so, my right side still weighs 90lbs. I did not increase it's weight though the base, my feet. It's just hanging out in space. The weight of my arm still travels through my no longer severed torso, down my legs and to my feet.
I'll see what Bert says, he is better with physics than I am. Possibly due to having more mass in motion than myself.