We need to be careful of the cause/effect of this. It's not that certain resonance structures are stable because they occur most often, but that the resonance structures that represent the most stable state of a molecule occur most often.
Molecules always strive for achieving the minimum energy, whether through electronic relaxations, electron delocalization, or other processes.
Minimum energy is analogous to not drinking too much coffee in the morning. If you drink too much coffee in the morning, you might get too hyper over the course of the day, and I don't think anyone really wants to be overly hyper. So, you drink the minimum amount of coffee so you can just stay awake.
Similarly, molecules don't want to be overly excited/hyper, and instead want to achieve the minimum energy, or ground-state energy.
Delocalizing the electrons in a system with many #pi# electrons helps make that happen in molecules that we draw as resonance structures. The more room (orbitals) the electrons have available to move, the more distributed their kinetic energy can be, and in some sense, the less energy "buildup" there would be in select orbitals.
You can also analogize electron delocalization with glasses of water. To achieve the smallest amount of water in multiple glasses, you should get the same amount in all glasses, not pour it all into one glass.
So overall, that's why resonance structures that represent the most stable state of a molecule are the ones that occur most often.