Your questions both relate to the effects of secret sins. In "The Scarlet Letter" there is irony to the title as the focus of Hawthorne is upon the secret sins that the Puritans withheld from society rather than the acknowledged ones.
At their meeting in Chapter XIV, Chillingworth tellls Hester that by her "first step" she planted the germ of evil. He says that although he is not fiend-like, he has "snatched a fiend's office from his hands....Let the black flower blossom as it may!" Chillingworth admits that he once had a human heart, but he has "become a fiend for his [Dimmesdale's] torment." Chillingworth has sinned greatly, having violated the sanctity of the human heart.
The worm of malevolence has eaten into the soul of Chillingworth and is evidenced in his decaying physical appearance just as the beauty of Hester's hair and complexion have diminished with her deprivation of human contact. Also, Dimmesdale's health has deteriorated from psychological torture both by his conscience and by Chillingworth whose influence has been "dwelling on him as a curse."
There is a phenomenon that occurs with those whose minds are so fixed upon an idea that it is somehow evidenced on their physical aspect. With Dimmesdale, Hawthorne suggests this phenomenon: "It was revealed." Since there is a singleness denoted by "it," readers have assumed that the minister has an A just as on Hester.
Chillingworth has become more deformed as the minister's health fails. Although Hawthorne does not give a direct reason, one can assume that he is eaten up with bitterness and anger. We know know that those emotions can have a negative effect on both health and appearance. Since he seems to focus solely on revenge against Dimmesdale, he has no true intimacy in his life and no social support system. Hawthorne, being ahead of his time, implies that the physical changes in Dimmedale are his body's response to his focus on continual hatred. As for Dimmesdale, Hawthorne does not immediately reveal what was on Dimmesdale's chest. However, during the last scaffold scene, Hawthorne reports that many people saw the letter "A" carved or burned on Dimmesdale's chest. This would have been something Dimmesdale did himself and a result of his shame at having fathered Hester's child. The critical difference was that Hester's "A" was open for all to see and Dimmesdale's was hidden until the very end.
As time goes on, throughout the novel, and Hester becomes more repentant, both Dimmesdale and Chillingworth continually suffer through the years. Dimmesdale has committed a grave sin in the sight of the Puritan community; yet, so has Chillingworth, although it is not as visible.
As Chillingworth continually stays Dimmesdale's healer, his character begins to change. He is so overcome with the chance to get revenge for the sin Dimmesdale has committed with his wife and continuing to cover it up, that his entire appeareance begins to change. He is so caught up in making sure that Dimmesdale suffers for his sin, that he is unaware that he too is suffering because he is so consumed with keeping up with Dimmesdale and the actions in which he is participating.
As one becomes so consumed with another's guilt, in an effort to get revenge, the entire soul is consumed and the only things they can focus on is the particular person and his/her guilt. This is exactly what happened to Chillingworth. He became so consumed that his appearance began to change. He became more ugly and hard-hearterd towards everything around him.