The answear is between chapters 9 and 12
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"The use of the term "leech" to describe Chillingworth is at once appropriate and ironic. After all, he is a physician, and leeches at the time were used in order to facilitate bloodletting. At the same time, however, Hawthorne is obviously suggesting the parasitic relationship between Chillingworth and Dimmesdale. We return to our earlier postulation that Chillingworth goes after Dimmesdale not because he is a stock character or out of any sense of moral purpose, but rather in an effort to absorb the reverend's virility, to steal his life force and appropriate it as his own, both in vengeance and for his own sake. Chillingworth realizes that he is old, deformed, and unworthy of Hester, even though he is her husband. Yet, he seems to retain the unconscious desire that if he can somehow capture Dimmesdale's spirit, he will be able to gain Hester's love and allegiance."