"I, and yourself. and possibly millions of others believe that the body weight will be equally divided between the heel of the front foot and the ball of the back foot."
This is probably only true in the small sort of walk performed as an exercise. The more dynamic actions which becomes possible when the walk-like action is preceded and/or followed by a body swing tend, in my observation, to go to far for the weight to ever be split between feet.
"And that on a backward step the supporting heel will not lower untill the moving foot draws level."
This is true for some actions, but untrue for others. In many lowering actions for examply, it is appropriate for the foot to go flat before the other foot has closed to it. Not for the body weight to run away too soon, but just for the foot to go flat and the knee to start absorbing some of the lowering, before the feet have closed. In flatter actions, such as the textbook walk, the heel will lower closer to the time when the feet pass. Different situations require DIFFERENT DETAILS.
"To S Q Q. Very nicely written . Others would do well to print that one and keep it as a reference, especially Anonymous."
SQQ is right that the body can only be supported in the unbalanced positions by also driving to create a horizontal acceleration. However, there are two important points to keep in mind:
1) The body is not necessairly fully supported. Some of these actions involve a marked lowering of the body!
2) The pulsing of acceleration and deceleration that this explanation applies can not usually be seen to occur on each step. Instead, it occurs only over each cycle of steps. Note that we never take two identical steps in a row in the swing dances, generally we have a heel lead, an upswing onto a toe, and a downswing onto a toe that then flattens. There is no per-step pulsing, instead the pulsing of the heel lead step gets smoothly blended into what precedes and what follows it - it becomes a trend rather than a pulse. Even when we have two heel leads in a row in the three step, they aren't the same - one builds into the next. The cycle always spans several steps.
As has been written before. It is to some hard to come to grips with the fact that they have been taught wrong. I was taught wrong at the bronze level in Latin in the Rumba. But i was not silly enough not to change when i found out i had been taught by somebody who should not have been teaching Latin at all. Nothing was said about the Latin Motion. Nothing about straight locked knees when the technique called for it. In fact most of what was taught was worse than usless.