Aileron

Continuing through my misconceptions dispelled since I started studying aviation… The big wings of an airplane hold up the body and the little wings hold up the tail.

This sounds reasonable enough, but imagine something like a common 737 while it's sitting on the ground. It has main landing gear under the main wings and then there is a smaller landing gear under the nose. This means its center of gravity (CG) is actually forward of the main wings; the aircraft is nose-heavy. It doesn't need anything to hold its tail (empennage) up, it needs something to hold its tail down.

The little wings (horizontal stabilizers) actually exert a down force during flight. This is a stability feature so that it's easier to get an aircraft's nose down to gain airspeed than to get its nose up towards a stall. It's also interesting that in level flight, the main wings have to not only counter the weight of the aircraft, but also the down force of the horizontal stabilizers.