One is a fascination with the celebrity he has become: an encounter with Mr. Weiner on the street is an event that other candidates cannot replicate, given his fame and outsize personality.

Another factor is his aggressive manner — those who have watched him say he seems ready to fight for their needs.

But other voters say it is Mr. Weiner’s flaws, and his attempts to make peace with the past, that are making them take notice.

“He sounds honest, in spite of what happened,” said Regina McClean, 56, a legal secretary who lives in Jamaica, Queens. “He has a humble spirit to him. We have to forgive and forget.”…

“I’m more vulnerable in kind of this weird way,” he said during an interview last weekend at a restaurant in Midtown Manhattan. “They’ve seen so deep into my personal life, I hate to say it.”