Why do many light aircraft have a trim tab on one side of the elevator only?
A small propeller driven plane like that will have a bit of adverse yaw, rolling to the left, because of propeller effects (P-Factor, slipstream, torque, etc)

The trim tab's effect is minimal because it is very small and is close to the centerline of the plane.  Any drag it creates causes a slight roll and yaw to the right, specifically to counteract the propeller effects.

That keeps the overall effect almost un-detectable.