"do not understand how the weight is not centralized at the extent of the walk. What about the side step? How much weight is carried into these steps? On any walk does the foot arrive into its position with the body weight over the foot?"
Generally, yes, - by the time the foot is placed, the body weight will already be ready to get on it.
"If so, does this mean the body stops moving until the other foot closes under the body?"
No, the body keeps moving - usually it projects beyond the standing foot a bit before the moving foot has closed.
Obviously the action in tango is rather different.