I agree pretty much with BMatthews. There are a lot of considerations in balancing a control surface. Some are to ease the stick pressure, some are for flutter prevention, some are for both. A claasic example of the counterweighted surface is the P-38 elevator, which was huge, and had a resultant high stick pressure due to the airflow over it. The counterweight in the middle doesn't really "counterbalance" as much as it just shifts the balance point further forward, relieving some of the effort required to move it at higher airspeeds. The other purpose was to shift the center of pressure to help reduce the incidence of flutter. However, it did nothing for the problems of compressibility in high speed dives which placed a shock wave at the hinge point and acted to "freeze" the elevator, This problem on the -38 was only corrected after a dive flap was added to the wing to limit dive speed below the speed where compressibility became a problem.

The triangular plates on an aerobat are called spades and are a variation on the balanced control surface like BMatthews points out on a Cub. When an aileron with spades is deflected, the spade has a force placed on it by the airstream in opposition to the the force on the aileron, lessening the stick force required to move the control surface, which translates to less fatigue to the pilot and quicker , more neutral control response. Spades ideally counteract input pressures to the point that the aileron will stay where it's put; this reduces the "feel" to zero, which some pilots like and some don't, so most of the time spade size varies to the pilot's preference. Most general aviation craft don't require counterbalancing, at least on all their controls, because they either have some power assist or their performance doesn't warrant it (it may be that the airspeed where flutter may occur is beyond the Vne of the aircraft)