Weiner's criminal acts, if convicted in a court of law, would warrant inclusion on New York's sex offender registry. While it doesn't sound like much, sending your private parts to a minor is considered a PREDATORY crime. In fact, anyone who did NOT solicit or accept such a picture can actually file charges.
The level three designation comes from the 17-year old girl's receipt of the junk. This could probably be reduced to a Level 2, but with additional charges and convictions from other sources, the NY Attorney General's office would be hard pressed not to make Weiner Level 3.
I actually don't agree that people like Weiner should be on the registry for the most part, just highly monitored by police (my wife is a compliance tech in California, so I sometimes go on her runs). But existing laws prevail, and Weiner could be looking at something far more serious that being laughed out of Congress.
(Ironically, it is the law that he championed that may be his undoing. He sponsored the KIDS act, designed to keep sex offenders off the Internet. Strange that his GOP counterpart, Mark Foley, sponsored the AWA act, and he was kicked out of congress for sex emails with underaged staff.)