The story continues
Your pre-flop raise told a story of strength. When the flop checks through to you, a continuation bet repeats the story — and it works even when you missed, because your caller must hold a piece of the board to continue, and boards miss everyone about two-thirds of the time. On the king-high board in front of you, ace-king makes the story literally true: the c-bet is value and narrative at once, which is why it deserves a full-sized wager.