Each of these characters deals differently with the restraints of Puritanism, showing Hawthorne's own conflict with the religious past of his family. Dimmesdale tries to hide his sin, knowing the consequences for confessing. Ultimately, his guilt and repression eat away at him, leading to his death. In fact, Hawthorne seems to judge Dimmesdale harsher than Hester because Dimmesdale denies himself for the sake of religious piousness. Chillingworth seems to deny the regulations of Puritanism all together. He pursues his own personal revenge, going against the biblical principle that revenge is to be left to God. He also suffers the consequences for this rebellion, as his desire to revenge consumes him. Finally, there is Hester's response to the confines of Puritanism. Hester boldly bears the public shame that Puritanism called for, wearing the mark of her sin with a sort of pride. She maintains her individuality, refusing to succumb to the overbearing social regulations of the time. Hester seems to overcome Puritanism without completely rebelling against it, as Chillingworth did, and is therefore able to live out her life as a part of society without sacrificing herself for it.
I'll try to keep my answer brief.
The strict Puritan codes make Dimmesdale cold, fearful, and self-centered. He cares more about public exposure and guilt than he does about Hester and Pearl. His ignorance of Pearl in public situations shows how fear of punishment is stronger than love for his own flesh-and-blood daughter. He manages to break free of his Puritan heritage at the end of the book, but at the cost of his physical life. I think Hawthorne is saying that his physical frailty was a mirror of his spiritual malaise--his heart died long before he did physically, thanks to Puritan overstrictness.
Hester's wayward, passionate nature was made even more rebellious than it would have been if the Puritan social codes were not so strict. She--like many young women of her time--was betrothed to an old man twice her age (at least) with no hope of divorce and (as far as we know) with no say in the matter. Hawthorne makes it clear in the opening Prison House chapter that she and the other criminals might not have broken the Puritan laws had they not been so strict, stern, and judgmental.
Chillingworth is the most obvious example of the effect of Puritan social codes. He is obsessed with guilt, punishment, and revenge. He is the wronged husband and according to Puritan social codes deserves to be avenged. Hawthorne shows how his obsession with making Dimmesdale suffer in the name of "justice" and "punishment" ultimately destroys his own soul. Chillingworth's physical deformity--like Dimmesdale's physical frailty--is meant to symbolize the smallness and deformity of a sick soul.
In all three cases, Hawthorne displays that the Puritan social codes were too strict. He expresses the apparent belief that social codes need to be less strict, less punitive, and more progressive.