Chillingworth, or Roger Prynne, enacts psychological warfare on Arthur Dimmesdale because he feels that Dimmesdale has cuckolded him. Chillingworth is jealous of the love that Hester has for Dimmesdale and disgusted that Dimmesdale will not confess that he is Pearl's father.
His acts of psychological torture against Dimmesdale includes becoming his medical adviser, seen in chapters nine and ten. The two men move in together and spend a great deal of time in each other's company. Chillingworth works to win Dimmesdale's trust, hoping that he will unburden himself and confess his sin. They have long conversations about the sins of other men, and Chillingworth opines that men's spiritual sickness manifests physically, implying that Dimmesdale's fading health is the result of his hidden sinfulness.
Chillingworth never goes so far as to overtly accuse Dimmesdale, but he becomes adept at playing on Dimmesdale's psychological weaknesses and persistently trying to get him to admit what he has done. Since Dimmesdale is a Puritan and deeply understands their beliefs about how God punishes sinners, Chillingworth's subtle manipulations are effective. His cruelty intensifies the anxiety Dimmesdale feels about eternal punishment, to say nothing of the guilt he feels about leaving Hester and Pearl to fend for themselves in a hostile community and his hypocrisy in leading a congregation.