raise, plan, project, behavior, actions
舉 centers on lifting something up, both physically and metaphorically: raising an object, putting forward a plan or project, and by extension, the actions or behavior one puts forth.
舉 is the traditional form of 挙. It combines 與 (likely contributing the sound) with 手 (hand) underneath, suggesting the idea of raising with the hands. The modern Japanese simplified form 挙 reduces the upper component.
The lower part is 手 (hand), and the upper part 與 looks like a heavy object being lifted. Picture several hands working together to raise a large plan or project upward.
For キョ, imagine a key organizer raising a giant key to start a project: key -> キョ, and the hand lifts the plan into action.