Former Rep. Anthony Weiner’s (D-N.Y.) friends believe that, while his campaign for mayor may have become a joke, it will set him up for a future political comeback. New York voters puzzle over why Weiner stays in the race despite constant ridicule. The city’s tabloids pump out streams of headlines punning on his name while late-night comics have made him a national punch line. Instead of dropping out, Weiner has embraced the media maelstrom in a calculated gamble that voters would respect his toughness and dedication to their issues. A new documentary by Stateless Media captures Weiner’s unorthodox campaign strategy,...