I don't see Weiner resigning, though. He is too vain, too stupid, too stubborn and too tone deaf to do so.
He will need to be forcibly removed.
Exception 1: Perhaps if MSNBC or CNN offer him a gig he will resign. This is a long shot, though, because Weiner is currently radioactive. He will need to spend some unknown amount of time wandering in the wilderness. Spitzer did this before he got his CNN gig. Marv Albert also did this before he was allowed to return to the sports media.
Exception 2: He will resign if the ethics investigation includes (as it probably will) multiple interviews with the FBI. Before this happens his attorney will explain the inherent risks involved (Scooter Libby) and if Weiner is smart (all evidence to the contrary) he will split before this happens. If he sez anything at all that is at odds with the truth he will be prosecuted for lying to federal investigators. And that will be all she wrote.
Likely scenarios if he doesn't resign:
The Democrats eliminate his congressional seat via redistricting.
They primary his ass.
To their credit, the Democrats are giving him some pretty strong hints that he needs to resign. Weiner just can't make the mental connection, though.
(That's the REAL story here...that the Democrats aren't circling the wagons and protecting his ass. The last time that the Democrats publicly shunned a member was when James Trafficant was convicted of taking bribes, filing false tax returns, racketeering, and forcing his aides to perform chores at his farm in Ohio and on his houseboat in Washington, D.C. And let's face it: The Democrats didn't like him. They hated him with an intensity that rivaled the sun. Weiner wasn't publicly hated by his fellow Democrats but they really, really privately despised him for his grandstanding on the floor of the House and for his Schumer-like camera/microphone hogging behavior. Weiner apparently believed in the "rather be respected (or feared) than loved" lifestyle and that works out real well until you need friends.)