I'm watching The Wire and in the Wikipedia article about one of the characters (Wallace) it is written "He betrays his age when he is found playing with toys while supposed to be on lookout duty."
I have not found any explanation of this idiom to betray your age anywhere on the Internet. I see it in two opposite ways:
1) To behave as you were younger than you really are. Explanation: Wallace was 16 years old and he was playing with toys which was inappropriate for this age.
2) To reveal your age. As if your age was an entity and it asked you to hide itself, but you revealed it in your behavior. Explanation: Wallace despite his age was supposed to be serious given that he was assisting drug dealers, but everyone saw that he was really a 16 years old boy when he was found playing with toys.