The Scarlet Letter 14

The Scarlet Letter

Chapter Thirteen

Entry Fourteen

In the thirteenth chapter, Hester's place in the society changes. People start to look at her differently, still with the knowledge that she sinned, but they let her enter their world a little more. Instead of identifying the "A" with "Adultery" it suddenly means "Able". People respect the strength she shows to get out of her misery by working a lot with her needle.

Furthermore, Hester realizes how much Dimmesdale suffers under the big secret. It's not his mind that's affected but his body that gets weaker and weaker.

"His moral force was abased into more than childish weakness. It grovelled helpless on the ground, even while his intellectual faculties     retained their pristine strength, or had perhaps acquired a morbid energy, which disease only could have given them."

I think you can interpret it as a sort of self inflected injury.
Both Hester and Dimmesdale have a guilty conscience because Hester thinks she should help Arthur by revealing Chillingworth's real identity and Dimmesdale thinks he should step out of the shadow to be indicted too.

So Hester believes she has to help him because

"Hester saw—or seemed to see—that there lay a responsibility upon her, in reference to the clergyman, which she owed to no other, nor to the whole world besides."