Hmm... no I'm not moving my center. I'm standing straight and centered. My spine and head is aligned and my diaphragm in flat. Weight does not shift and I've let it rest at the center of my soles. Perhaps I've got the arms positioning wrong.
After what you mentioned about me using visual clues I elected to close my eyes and try to sense a shift in weight. I did this because I know that I do have balance issues when standing on one leg with my eyes closed. So I believe that a lot of my balance does come from visual stimulus. But no, there's no change in weight even with my eyes closed.
Well, you are compensating somewhere in your structure. Find out where and you will have identified the source of a large part of whatever your concern may be, I would say.
Going from just palm up full extension to palm down full extension at this here computer screen in front of me gets me touching the screen from 2 1/2 inches out statically erect. In the past I have clipped a laser pointer to my shirt lapel to verify there was no fore-aft torso movement involved in the extension. That's why the straight punch twists in the same way, to release full structural extension of the limb. But the same is true of the whole structure.
An actuation of this structural mechanism allows expansive and contractive movement of the body without creating levers and the waste of energy and structure compensating for inherent shear . If sharply done and released it creates surprisingly fast movement of the limbs in a manner that is not "push/pull" (i.e. -- not leveraged).
It is also the manner of deep reflexive actions -- if your hand ever touched a hot stove you snatched it back -- like a weight on a wire -- by this precise mechanism, generated by a spinal reflex -- and the inverse of that
is the infamous "no-inch" punch.