What does it mean if you just broke up and... ?

He's doing it because he's a free man. Sure, you live together until whoever is moving can move. But he has no obligation to you anymore. He is no longer partially responsible for your emotional fortitude. He can do whatever - or whomever - he wants. Now truth be told, he was probably looking at those sites all along before the break-up, he was just more discreet while you were together. This is PURE SPECULATION ON MY PART. Now that you have broken up, the only discretion he needs to use is when going home with a girl - it'd probably be best to go to HER place. Other than that, he owes you nothing. It's over. He's moving on. You should do the same.