Anthony Weiner, the beleaguered sexting scandal-plagued New York City mayoral candidate, may be trying to boost his poll numbers with a new documentary about his campaign. The New York Post reported that MTV filmmaker Josh Kreigman — who also used to work as Mr. Weiner’s congressional district director — has been following the candidate around his campaign trail, filming and recording every step of the way. He rides with the candidate. Meanwhile, Mr. Weiner always carried a black microphone box in his back pocket, The Post said. Campaign officials are coy about the taping, saying only that it’s not for...