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

The first hint we get about the meaning of the veil is the subject of the first sermon Mr. Hooper delivers after he begins to wear it. "The subject had reference to secret sin, and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness [...]." His congregation even feels that he's "discovered their hoarded iniquity of deed or thought."

Then, when his fiancee, Elizabeth, comes...

The first hint we get about the meaning of the veil is the subject of the first sermon Mr. Hooper delivers after he begins to wear it. "The subject had reference to secret sin, and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness [...]." His congregation even feels that he's "discovered their hoarded iniquity of deed or thought."

Then, when his fiancee, Elizabeth, comes to ask him about the veil, he says, "'If I hide my face for sorrow, there is cause enough, [...] and if I cover it for secret sin, what mortal might not do the same?'" So, we can piece together that Mr. Hooper's veil is symbolic of our attempts to hide our secret sins from one another. We all possess such sins, and yet we refuse to admit it to our fellows, and in this way we hold up a figurative veil between ourselves and everyone else.

Likewise, on his deathbed, Mr. Hooper asks, "'Why do you tremble at me alone? [...] Tremble also at each other! [....]  I look around me, and, lo! on every visage a Black Veil!'" He complains that he has been shunned because of his black veil, but that the quality that it signifies is possessed by everyone. If they find him frightening, then they ought to find each other just as frightening.