Not normal behavior? How many people know they've been cheated on before. How many people know their spouse has used the internet for all kinds of social sexual relief, like camming, sending emails, etc. Now how many people have a host of people actively trying to uncover all their dirty little secrets and release them into the world so they become common knowledge?
This behavior is VERY normal. It's causing an uproar because a significant number of normal behaviors carry social stigma (Hey there, nice to meet you, I'm gay). And it's not commonly seen in the public sector because most people keep personal information like this as secret as possible, wherever they can.
And I'm sure Weiner isn't so basic a human being that he has only one want or desire. This might shock you, but most people don't pursue one goal with single-minded focus. Weiner has many desires, among them are a political career and a sexual life that's a certain degree of poly-amorous.
Sure, his poly desires are problematic for public office, and his desires for public office are problematic for a poly lifestyle. But that's hardly the only thing he has to struggle with, and it's not like monogamous politicians don't have entire graveyards in their closet. Among these skeletons are hit wonders like "I hate Jews," "I was a Black Panther," "My dad was in the INLA" and "I'm brown."
And in the realm of relationships, there are plenty of choices Weiner could have made that would have realistically been just as damaging to his political career. He could have married a woman of color, he could have married a Catholic, he could have married an Iranian, etc.
It's not just sexually "deviant' behavior that's problematic for public office.
Sure, it's a problem for him. But it's also a problem for everyone else. What else would you call it when society creates a bunch of arbitrary social limits that we expect our politicians to abide by, even though they don't map to universally held sexuality, and in no way filter for effectiveness in public office?
Are you actually going to say that the society doesn't lose when we omit candidates for arbitrary reasons, rather than for having crappy policy and/or an ability to follow through/negotiate? It's possible Weiner is literally the perfect man for the job here (dunno, have no clue what his policies are), and there's a great chance he could lose because of something that has nothing to do with his ability to do the job.
I'd call that a huge problem for everyone else.