Almost everything my teacher says revolves around this idea of weight transference.
The reason why it is so effective is because it is the best and most logical way to bring out a melody, prevent fatigue, and play evenly.
In arpeggios, for example... the hand should feel as though it is falling to the left or right, and the elbow must move to catch it. A more vivid sense of this is when you stand up, lean forward...forward ....FORWARD....NOT moving the feet....eventually you will have the urge to fall forward and catch yourself with your foot stepping out. This is a natural reflex. If we can harness this reflex and apply it to the piano, we can play much more comfortably and truly feel free at the piano.
If I am nervous before a performance, the trembling fingers can be controlled by playing piano- putting my hands upon the keyboard like you would put hands on a table.
I believe weight transference is the key to making music, instead of "playing" piano like you would type on a computer keyboard.
donjuan