Larger cheek on one side
The causes of a larger appearing cheek can be due to differences in fat in the subq space, fat in the space below the masseter muscle, bony size differences or hypertrophy of the masseter. A board-certified plastic surgeon could evaluate you and make recommendations about how to make your face more symmetric. Good luck.
Why asymmetry ?
Good question. It turns out that all of us are born with our two sides being different. The difference may be more in some people than others but there is always a difference. If you study embryology and the development of the human face you will see that the two halves develop separately and meet in the middle. The way you move your mouth has nothing to do with the difference. People magazine many years ago even published mirror image faces of attractive people to improve symmetry. The results showed that slight asymmetry was more attractive than symmetry----- go figure. If you start analyzing unadulterated photos you will start to notice the differences. Bottom line, slight asymmetry is normal and in most cases attractive. And that my friends, is science.