When you gently shake a bag of chips, you can think of it as disturbing the positions of all of the chips a little bit in some random direction. Gravity means that if the new position of the chip is a place where it could fall, it will fall. Bigger chips can't fall through the gaps between chips below them, so it's unlikely that they will be disturbed into a position where they will fall. In contrast, small chips have many more places where they can fall through gaps, so for any given shake, the chances are much higher that they'll fall. Gently shake the bag a bunch of times, and you'll most likely have disturbed almost all of the small chips into gaps that the big chips can't fit into, which causes them to fall to the bottom of the bag.
Of course, if you vigorously shake the bag, then it's no longer just a small random disturbance. Instead, the position of every chip is basically completely randomized relative to its neighbors, which means that small chips and large chips generally suffer a similar fate. So vigorously shaking a bag where the small chips have already settled to the bottom would "reset" things such that some small chips were on top again.