It could be a number of things....
If the spindle hole is off center, that can certainly cause a meandering pitch.
If the motor isn't maintaining a stable speed, that can especially be noticeable on sustained piano notes as the pitch will waiver.
If your belt is stretched/worn, etc that can also contribute to the issue. Also, make sure that both the motor pulley and the subplatter that the belt goes around are clean.
Best wishes,
Don