It may seem rather obvious, but you want your horse to stay balanced under you when you ride. You don’t want to be behind the motion or listing to one side or the other.
The good news is that your horse wants to stay under you and actually will do its best to help you out by following your weight.
Years ago I had the privilege of riding with Dr. Max Gahwyler. He was the first “real” dressage instructor I’d ever had the chance to train with and he used to come to the New Canaan Mounted Troop to teach a few of us. I am forever indebted to his patience and good humor as he tried to explain some of the basic concepts of dressage to me.
He was the one who showed me how a horse will step under your weight as it shifts. To illustrate the concept he asked us to drop our reins and influence our horses by stepping more heavily in one stirrup or by weighting one seat bone. He asked us to make circles and change directions. It was both harder than it sounded and, once you got the concept and your horse was listening to you, easier.
Although we did it at a walk, it’s a principle that holds true at any gait. If you stay in the center of your horse, the way you shift your weight is an important aid. Of course, it still influences your horse even if your weight is shifting unintentionally. The problem then is you are probably just confusing the heck out of them!
It’s still something that I do when I am cooling out or riding in an open space on a long rein. Freedom is quite sensitive to my position and it helps me see how important it is that I stay still and secure so that I can influence him intentionally when I want him to move.