How do secrets play a role in "The Minister's Black Veil"?

Secrets play a major role in "The Minister's Black Veil"; there are the secret sins of the members of the congregation, sins they fear that the Reverend Mr. Hooper may see from behind his veil, and there are the possible sins that the minister himself may be hiding that also disturb the men and women. 
When Mr. Hooper approaches the meetinghouse,

[T]here was a general bustle, a rustling of women's gowns and shuffling of the men's feet, greatly at variance with that hushed repose which should attend the entrance of the minister.

Indeed, it is the fears of what Mr. Hooper may be looking at from behind his veil or what he may be hiding that disturbs the congregation when the minister passes, then mounts the pulpit, and afterwards as he continues to wear the veil. For, in demonstrating this sign of his own shame and melancholy to the world, Mr. Hooper indirectly forces his congregation to look inward and feel their own sins, secret sins they wish to hide. 
As time passes and Mr. Hooper refuses to take off the veil, the Puritans fear he hides some dark secret. Consequently, they shy away from the minister. One of the men remarks,

"The black veil, though it covers only our pastor's face, throws its influence over his whole person and makes him ghost-like from head to foot. Do you not feel it so?"

The members of Mr. Hooper's congregation are worried that he can see their sins, and because they think he does, the veil becomes "the symbol of a fearful secret between him and them." In reality, the veil disturbs Mr. Hooper, as well. 

He never willingly passed before a mirror or stooped to drink at a still fountain lest. . . he should be affrighted by himself.

When Elizabeth, his betrothed, asks him to remove the veil under threat of breaking their engagement, Mr. Hooper refuses, and even as he lies dying, the minister is adamant that he will not remove his veil. He tells those who ask him to take it from his face that when the friend does not hide the truth from his friend, when people do not shrink away from their Creator, "loathsomely treasuring up the secret of [their] sins," then he will be "the monster," and only then because until such time there is a veil covering all their faces, all their secret sins.