I remember one of my teachers telling me to relax my shoulders. I thought I was playing relaxed until my teacher pointed out that my shoulders were higher than normal. Pianistimo is right, sometimes you need another person watching you to tell you if you look tense or not. There are a lot of points in the body that we need to pay attention to, and sometimes we just overlook one part.
With regards to Bach, those were different instruments in his day. The harpsichord is much more delicate than the piano and is plucked with quills. There is no way to alter dynamics, and therefore no need for using added body weight as we do on the piano.
As others have mentioned, playing piano involves the whole body. As you advance in technique, pieces will start asking you to play with more dynamic contrasts. Especially in order to play loud, one directs one's own body weight through the fingers to get increased volume. Before you can do this, you have to start loosening up all those other body parts that need to be used.