Why are trailing-edge control surfaces usually split? I've noticed on many military and commercial jets, the trailing edge control surfaces (ailerons and flaps) are separate from each other.

Why is this? Can't both serve the same function? It would save weight and complexity if one combined control surface ran the length of the trailing edge, instead of being split in half.

A particular example I found is the F-102 Delta Dagger. There's no conventional tail to experience disrupted airflow, so why have separate ailerons and flaps?



A similar idea that I know exists is the V-tail, such as in the F-117, which has "ruddervators"---combined elevators/rudders. It can still control yaw and pitch at the same time by somehow averaging the deflections. Presumably, combining and averaging ailerons and flaps should be even simpler, since they're both deflecting on the same axis.
Same reason you have split ailerons on most big airliners. The inboard surfaces deflect at higher speeds and the outboard ones are locked, reducing the twisting (torque) forces on the wings. It also allows for finer control (in fly-by-wire cases) as well. Like a lever, a small deflection of the outboard surface results is higher rate pitch/roll (in this delta wing elevon example) compared to same deflection of the inboard surface.