Hawthorne uses the novel The Scarlet Letter to interpret and comment on human behavior. Hester shows us a woman who has committed a sin, but is not a sinful woman. Hawthorne uses her to demonstrate the hypocrisy of others and to show faith and devotion. Dimmesdale is demonstrative of the effect that grief and duplicity can have on the human body. Although Hester and Pearl thrive, he gets weaker and weaker.
Keeping with this theme, Chillingworth shows the effect of vengenance on the soul. Hester begs him to let go of his hate, but he will not. Thus, he becomes more monomaniacal and obsessive. Physically, he begins to look warped and grotesque. Besides showing the negative effect of holding a grudge, Chillingworth's purpose - like Dimmesdale's - is to demonstrate how emotions can manifest in the outward appearance of the body.
Chillingworth has a role of a victim in this story as well as punisher. Chillingworth takes a part of the blame for the sin, spelling things out a bit when he visits Hester in the jail cell. He left to pursue enlightenment outside of the colony and did not contact Hester at all. Also, he refers to their life before he left as not perfect, he was scholarly, she was his maid. This could be the reason why Hawthorne focuses on the Dimmesdale/Chillingworth connection.
As victim, he is the "one on whom was cheated" and asks not to be revealed to the colony as Hester's husband. If he were to reveal his true identity, Hester would be put to death, name of the father notwithstanding. Not to mention, he would forever carry the stigma of being the one who was not good enough to keep his wife from straying.
Chillingworth has a few roles in this story. Punishment is part of the story but it represents something greater. This punishment represents the hypocrisy of the puritan way of life. On the surface, Chillingworth comes across as a good person and a good friend to Dimmesdale and to the society on the surface, represents how all puritans should act. However, below the surface he is actually full of revenge and anger and is just as guilty as anyone else in the novel.
He represents not only hypocrisy, but also the dangers of hate a deceit. The question is, does Chillingworth have a right to decide on the proper punishment for another when he himself is not without sin. In the end, he dies like everyone else and is as miserable as anyone else.