Your standing leg sends your body.

Your body brings your moving leg along with it.

Thus the body does entirely control the moving leg, but the standing leg controls the body.

Yes, you actually do flight your body when you walk... just not enough to be very aware of, because we don't generally try to cover nearly as much ground walking as we do dancing - if we wanted to cover ground, we'd run, and running has LOTS of body flight. But also remember that dancing is walking with another body in front of you... you do have to make allowances for that, and body flight is one of these. (unless you switch to the tango style of movement, where the allowance is made by the diagonal nature of all the steps)