Hooper's veil is a clear sign that he is trying to make up for, or atone for, his sin. Hooper seems to imply that the veil is a symbol for all sin, or for the idea that we sin, itself. It is not just a sin or two of one person; all of humanity is a sinner. Hooper is a sinner too; he wants to show that he is not prideful, but that he is hiding his face. Now, in all reality, he is more visible due to the black veil. Did Hooper wear the veil to express his guilt at committing adultry? Did Hooper wear the veil to let others know that we are all sinners and that we cannot judge others - or we will be judged?
The veil may in be a symbol of a shadow that man tries to hide his sins behind, and as he quotes, "the saddest of all prisons is a person's own heart". You may be able to hide all the sin from others, but you cannot ever hide it from yourself. He saw himself in a mirror and did not like what he saw.
