From the American Council on Exercise: Bodyweight Squat. An excerpt:
The emphasis is in bold. Using good squat form, to emphasize the instruction in bold, try flexing your arch such that your feet feel like they are touching the floor primarily on the balls and heels of your feet. By exaggerating the arch and using the four points of the balls and heels, I have noticed smoother knee action and better balance down and up. You may already do this, or, may have a different experience. Use it if it works to make knee action smoother.
Try this near a wall for touch support. It can even be effective within rigid shoes as the shoes act as the floor. You may have a shoe fit problem if you cannot arch your feet within your shoes without impingement or discomfort.
See how this feels. Any difference?
REMEMBER NOT TO DO ANYTHING YOU WOULD NOT DO BECAUSE OF MEDICAL ADVICE, LIMITATION, CONDITION OR INJURY.