I became curious about this since reading a semi-fictional account of the Morgan horse. At one point, the owners of some thoroughbreds challenge the Morgan to a race, and they specify that their jockeys are 'large and heavy men.'
They mention this so the Morgan will also carry a full-sized rider in the challenge, and not a mere slip of a boy.
So when did this move toward small men and short stirrups begin, and was it gradual or sudden?