What evidence in the text hints at or suggests Mr. Hooper's reasons for wearing the black veil?

We never get to find out exactly why Mr. Hooper wears the black veil, which merely adds to its mystery. Nevertheless, there are one or two subtle hints in the text that point towards a possible answer. When his fiancee, Elizabeth, comes right out and asks him why he insists on wearing the veil, Mr. Hooper's response is cryptic:

"If it be a sign of mourning," replied Mr. Hooper, "I, perhaps, like most other mortals, have sorrows dark enough to be typified by a black veil."

Precisely what those dark sorrows are we do not know, and Hooper certainly doesn't care to elaborate. But at the very least we can surmise that the reverend has experienced a good deal of sadness in his life worthy of mourning. And as a black veil is traditionally a sign of mourning, he feels it entirely appropriate to wear one, even if it scares and unnerves virtually the whole of his congregation.
Even on his deathbed, Mr. Hooper refuses to spill the beans. But once again, there are hints. The suggestion is that Mr. Hooper harbors a secret sin that is a matter between him and his God. It would therefore be inappropriate to divulge what causes him to wear the veil. As he looks around him, everyone else appears to be wearing a black veil—i.e. has their own secret sin—but unlike Mr. Hooper they are not prepared to acknowledge their faults, choosing instead to castigate someone for wearing an unusual item of clothing:

"Why do you tremble at me alone?" cried he, turning his veiled face round the circle of pale spectators. "Tremble also at each other! Have men avoided me, and women shown no pity, and children screamed and fled, only for my black veil? What, but the mystery which it obscurely typifies, has made this piece of crape so awful? When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived, and die! I look around me, and, lo! on every visage a Black Veil!"