Should Anthony Weiner step down from running for mayor of New York City?

Anthony Weiner, who is running for mayor of New York City has been caught many times “sexting” nude pictures of himself to younger women. The women are over 18 years of age as far as I can tell. Here is one story on the subject. Mr. Weiner is married if that matters.
Do you think his sexploits should matter in his running for mayor? It is reported that he refuses to step down.