How does Dill mature in To Kill a Mockingbird?

Charles Harris Baker, known as Dill, matures after two incidents: (1) The cross-examination of Tom Robinson by Mr. Gilmer, and (2) his running away from home.

(1) After the heartless drilling of Tom by Mr. Gilmer and his exploitation of Tom's having said that he felt sorry for Mayella and accusing him of being impudent, Dill cries in reaction to what he perceives as Mr. Gilmer's talking to Tom in such a "hateful" way. "It...

Charles Harris Baker, known as Dill, matures after two incidents: (1) The cross-examination of Tom Robinson by Mr. Gilmer, and (2) his running away from home.

(1) After the heartless drilling of Tom by Mr. Gilmer and his exploitation of Tom's having said that he felt sorry for Mayella and accusing him of being impudent, Dill cries in reaction to what he perceives as Mr. Gilmer's talking to Tom in such a "hateful" way. "It just makes me sick," Dill says.
Mr. Dolphus Raymond consoles Dill to some extent, telling him that time will make him less "thin-hide[d]."
Later, Dill says cynically that he will become a clown:

"There ain't one thing in this world I can do about folks except laugh, so I'm gonna join the circus and laugh at them" (Ch.22)

His attitude is now more hardened as Mr. Raymond has said it would become. While this reaction does not demonstrate the best reaction, it, nevertheless, demonstrates a maturation in the sense that it shows Dill's efforts to reconcile things for himself.

(2) When Dill runs away from home, his action indicates a childish, emotional response to the hurt that he has felt in being alienated from his parents by being told to go and play with his things, or go outside.
After Jem informs Atticus that Dill is in the house, Atticus tells Dill the boy that he must let his parents know where he is. Also, Atticus notifies Aunt Rachel, who flies into her "Do-oo Je-sus" exclamation.
With maturity, however, Dill "bore with fortitude" her "Wait Till I Get You Home Your Folks Are Out of Their Minds Worryin'" and when she is finished scolding Dill, Dill smiles when she tells him he can stay overnight with Jem and Scout and he "returned the hug at long last bestowed upon him," demonstrating his maturity in not holding a grudge against his aunt for all the scolding he has received.