Chillingworth has been trained in healing by the Native Americans, although he really isn't a doctor. None-the-less, he couldn't have chosen a better occupation to impersonate. What he knows certainly comes in handy.......... I believe that Hawthorne's use of "physician" and "leech" connotates what he's doing rather than what he is. He's learned enough to get by as the physician, but he act the leech with Dimmesdale, keeping so close to the man that he's almost attached. Leeches are blood-suckers; they suck the life right out of you...... this was what Chillingworth hoped to do with Dimmesdale.