Chapters 9-12

Mr. Mahoney, I hate to break it to you because I know how big of a Chillinworth fan you are, but chapters 9 through 12 made me creeped out, annoyed and a bit loathing of him. What has been standing out to me throughout the novel is the association Hawthorne gives between Satan and Chillingworth, and it was these chapters that embody it the most thus far. (especially bottom of pg 126) Much of these chapters develop the relationship between Chillingworth and Dimmesdale. Chillingworth now lives with the reverend under the pretext of a desire to heal him, however, in reality, Roger is seeking analyze and destroy the man. On page 118 Hawthorne describes the doctor's eyes as having a "light glimmering...burning blue and ominous." There is evil in Roger Chillingworth's "friendly" actions toward Dimmesdale. Though he does not fully understand why, the reverend senses this malevolence in their friendship, but the physician hides it well. Dimmesdale is intuitively concerned but when he looks at Chillingworth, "There the physician [sits]: his kind, watchful, sympathizing, but never intrusive friend" (Hawthorne 118). Roger is actually very intrusive in subtle, manipulative ways that Dimmesdale does not consciously notice. For instance, Roger prompts a conversation (pg120) about Hester, sin and secrecy with Dimmesdale in order instill terrible guilt in the reverend because he believes that he is Hester's partner in adultery. While appearing sympathizing, Roger is really dissecting Dimmesdale's responses for information and literally killing him with guilt.

Also, I interpreted from these chapters that the scaffold holds a similar but slightly different meaning and symbolism for Hester and Dimmesdale. For Hester, the scaffold is a symbol of the shame she was subjected publicly by the puritans years ago and also the public shame sh continues to feel as a result. For Dimmesdale however, the scaffold is a symbol of guilt, a more internal disapproval of himself that is not known to others. He is not subjected to shame but he is the victim of guilt. 

What actions does Dimmesdale take to punish himself?
Dimmesdale keeps a secret whip in his closet which he violently whips himself with as a form of punishment for his sins. In addition to this, he fasts for the same reason. He does not fast like others to cleanse his body, but instead he fasts until he can no longer even stand as a means of self punishment. (pg 132)

Why is Chillingworth called a "leech," and why, at another point, does the narrator compare him to  a miner?
First of all I love that Hawthorne chooses to call Chillingworth a leech because it has a double meaning. Roger is literally a leech because at that time "leech" was a word which referred to physicians because there was a practice which involved using leeches to drain blood to heal people.In a more figurative sense, Chillingworth is a leech because he has attached himself to Dimmesdale in a destructive, parasitical manner. The way Chillingworth subtly tortures Dimmesdale literally drains life from him in the way a leech does. Day by day, Dimmesdale looks more emaciated and closer to death.
The narrator also compares Chillingworth to a miner. This is an accurate comparison because, like a miner, Chillingworth is in search of something very specific and something of great value to him. He searches and searches in manipulative ways to find an answer like a miner digs and digs to find gold or coal etc.