The best starting point for understanding the bizarre controversy surrounding Anthony Weiner is this great 2001 Vanity Fair story about the culture of interns and exploitative sex on Capitol Hill:

The women are heckled as they enter. “Tell us your name and where you are from,” says one of the men. As if on a game show the women comply, one by one. When Caroline says she is an intern, the largest of the group, a white-haired man with a big belly and big laugh, roars, “We’re afraid of interns.” He throws his knife at a lean man named Mike, at the other end of the table. Mike is unamused. He threatens to throw it back. Another guy, rotund and jolly-faced, stands up and does an impression of Marlon Brando doing Don Corleone. The others think it’s hysterical.
Diana whispers that there is no way they can be congressmen. She figures they are businessmen. She wonders how she is going to get out.
They are congressmen—although at first they pretend not to be. One, the youngest, with a tiny goatee, introduces himself as Anthony, an auto-parts salesman. The others call him “the Jewish kid” and make fun of his beard. Their real names and states are as follows: the auto-parts salesman is Anthony Weiner (D-N.Y.); the lean Mike is Michael Capuano (D-Mass.); the jolly guy who imitated Brando is John Larson (D-Conn.); the man who was worried about interns is Robert Brady (D-Pa.). ...
The next day, New York’s Anthony Weiner finds the time to hunt down Diana’s E-mail address. He writes that he hopes they might meet again. Diana is overwhelmed that he’s managed to think of her on a day that must be heavy with import and emotional intensity. Last night he mentioned that he’d be going to Manhattan to inspect the World Trade Center wreckage with the president. They’d be traveling together on Air Force One.
Caroline records: “Went for lunch with Diana. Anthony Weiner has emailed her and she didn’t know he was a member of Congress. She died when I showed her his card! It was so funny!! I think she likes him, but she doesn’t want to admit it. In fact, I know she likes him ’cos she’s been on his website this afternoon looking at the photo gallery.”
A week later, two nights before Caroline will leave for England, the girls return to the Capital Grille. Now they know the drill, and they capture their prey with ease. “Three more congressmen,” Diana gloats. “Republicans—got their cards and everything.”
She has left Anthony Weiner dangling, after he E-mailed her that she should come and visit his office “in person.” “I thought that was kind of cheesy,” sniffs Diana.

Now here is the tricky part. Understanding Weiner's character makes it very easy to believe that he would tweet a lewd photo to a young woman. On the other hand, it also makes it easy to believe he didn't tweet the photo but is refusing to explain himself because he did some other embarrassing or unethical act. The upshot is that the allegation against him seems a little sketchy, but it's hard to generate much sympathy for the man.