The reasons Anthony Weiner will not affect the chances of Hillary Clinton becoming president are twofold, despite the concerns of an "analyst" interviewed by CBS News ("Analyst: Weiner An 'Irritation' For Possible Clinton 2016 Campaign). One: November 2016 is three years and two months after people stop caring about Anthony Weiner. And, two: Anthony Weiner doesn't reinforce the things that people don't like about Hillary Clinton.
Consider, in contrast, Reverend Jeremiah Wright. The reason that Wright became an issue for candidate Barack Obama in 2008 was that the caricatured version of him was the embodiment of what some voters feared in an Obama presidency: an angry black man, biding his time until he could make white people pay. Both that fear and the caricature itself were deeply racist, of course, which was the real problem for Obama. It's why his now-famous Philadelphia speech was about race, not Wright. But Wright offered Obama critics with something to point to, a black person yelling "God damn, America," a proxy with a face.
Bill Ayers, meanwhile, served as proxy for the other fear: that Obama was a socialist that hated America. Ayers, who by 2008 was a college professor who'd put out a few books, was a member of The Weather Underground in the 1960s and '70s. He participated in the development of plans for terroristic action, avoiding prison because the FBI violated constitutional protections in researching the crimes. Some in the generation defined by the protests over the Vietnam War saw Ayers as the embodiment of a particular political activism — one they worried that Obama, with his community organizer roots, sympathized with.
Ayers and Wright, in other words, both gave opponents of Obama something to point to. "This," they could say, "is what we're worried about."
For Clinton, that's not a worry. No one is going to argue that the tenuous relationship between Hillary Clinton and Anthony Weiner is suggestive that Clinton will obfuscate or misbehave while in office. People may think she will, but not because her staffer married a guy who's an idiot. People will have plenty of reasons to be skeptical of a Hillary Clinton presidency, all of which exist independent of Weiner.
If, on the other hand, Clinton were linked to someone whose behavior better reinforced those existing concerns, Clinton might be in more trouble. Had Weiner, say, been implicated in masking a failed government operation of some sort — and, worse, had Hillary known about it — critics might use that as a reason to question what happened at the embassy in Benghazi. (Again.)
By 2016, Anthony Weiner will (almost certainly) have been working in the private sector for several years, perhaps helping position his wife Huma Abedin as she considered running for office. Should Clinton run, and Abedin help, Weiner will come up again, but probably as a nostalgic blip, the way we thought about him until April of this year. Clinton's fortunes are her own; Weiner only an anchor to himself.
If it were Bill Clinton running, though: different story.