When considering shot size and pellet dispersion, this is more to do with momentum than direct force application. Momentum is directly governed by mass and velocity so if you alter the mass of the projectile, you alter its ability to maintain its directional momentum. The obvious example here is of a bowling ball holding its trajectory better than say, a tennis ball in a bowling alley. The increased mass gives the bowling ball more momentum to travel in a single trajectory and makes it less susceptible to other forces such as cross winds or, depending where you bowl, other balls coming across your lane...
Which leads us nicely onto shot travelling down a barrel.
Heavier shot can maintain forward momentum better than lighter shot and, when you add in the additional pellet count you get with smaller shot, you create more collisions and external forces to amplify the dispersion effect (or deviation to the original directional momentum) with lighter shot.
The net result of all this is that you see the results Will gets one his pattern plate.
Please, let's not now get involved with pellet deformation, aerodynamics etc etc