The leech, Roger Chillingworth does indeed function figuratively as described above. In another sense, Roger will not let go of this situation just like a leech gets stuck to host through the power of suction. He is bound and determined to get the two sinners to confess the name of the father of the child.
Chillingworth, having this great pursuit, takes residence in the town. Hawthorne points out that this is of great significance because of Chillingworth's abilities. Doctors of his capability often settled a lot closer to Boston wherein there would be a great body of people to serve as well as schools of medicine to take up instruction.
Likewise, Chillingworth is well on in years.
This learned stranger was exemplary, as regarded, at least, the outward forms of a religious life, and, early after his arrival, had chosen for his spiritual guide the Reverend Mr. Dimmsdale.
People understood him to be an experienced and intellectual man. He was an admired practitioner of faith. Yet among these great qualities, he chose a timid and young spiritual mentor. This is odd. He attached himself to this young man and must have a reason for it.
About this period, however, the health of Mr. Dimmsdale had evidently begun to fail.
Conveniently, the young reverend had very recently made the acquaintance of a leech. The ill in him is doing him more harm than good, just like the effort of leeches in those days to indeed suck out the 'bad blood.'