Anthony Weiner formally announced that he will run for mayor in New York City in a video late Tuesday, reports Aaron Blake:

The former congressman asks for “a second chance” and prominently features his family, including wife Huma Abedin.

“Look, I made some big mistakes, and I let a lot of people down,” Weiner, a Democrat, says after outlining his platform of a more affordable New York. “But I’ve also learned some tough lessons. I’m running for mayor because I’ve been fighting for the middle class and those struggling to make it my entire life. And I hope I get a second chance to work for you.”

Abedin closes the add by saying: “We love this city, and no one will work harder to make it better than Anthony.”

The mistakes to which the former Democratic congressman refers in the video are the lewd pictures of himself he posted to the Internet while he was in office, as the Associated Press recounts:

After a photo of a man’s bulging, underwear-clad groin appeared on his Twitter account in 2011, he initially claimed his account had been hacked. After more photos emerged — including one of him bare-chested in his congressional office — the married congressman eventually owned up to exchanging racy messages with several women, saying he’d never met any of them. He soon resigned.

In recent interviews, he has said he shouldn’t have lied but did it because he wanted to keep the truth from his then-pregnant wife, Huma Abedin, a longtime aide to former secretary of state Hillary Rodham Clinton. She told the New York Times Magazine that she has forgiven him. (Continue reading here.)

Some have compared Weiner to Mark Sanford, who finished his term as governor of South Carolina in disgrace after an extramarital affair became public. When Sanford won a congressional election in that state this month, Sean Sullivan wrote that a similar recovery would be much more difficult for Weiner:

Weiner would be aiming very high. Being mayor of New York City is one of the highest-profile political positions in America. It’s a step — if not several — up from where he was in Congress. We’re not talking about a comeback of baby steps here. It’s hard to ask voters for what would essentially be a promotion after resigning under a dark cloud.

Secondly, Weiner wouldn’t have the benefit of being an immediate front-runner for his party’s nomination. That title belong to Christine Quinn, the City Council speaker whose formidable infrastructure will be tough to match and who, polls show, has jumped out to an early lead. (Read more here.)

Even if Weiner doesn’t win, his entry could still have consequences, Chris Cillizza writes:

Weiner’s entrance into the race virtually ensures that no candidate will get the 40 percent of the primary vote needed to avoid a runoff.

“He guarantees a runoff but doesn’t guarantee his own place in that runoff,” said one Democratic consultant who keeps a close eye on politics in New York City. “It looks to be a major gift to [former NYC Comptroller] Bill Thompson [who is] running the slow but steady race while Quinn is the hare.” . . .

The other obvious impact of Weiner’s candidacy — and we strongly suspect this is why he is really running — is to wash himself clean in the eyes of the electorate. As in, this bid is less about Weiner winning (he is smart enough politically to know it’s a major long shot) than about him withstanding all of the bad stories, punny headlines and ridicule so that when he runs again for office (and he will run again) he can say: “Look, we covered all of this ground in 2013.” (Read the rest at The Fix.)