Thank you all for your support and input!!

He's now contradicted himself and tells me he's not talking to women, so i am now confused. We are going to talk it through today on the phone. I agree about not having sex with him if he's still browsing. I can (I think) continue to date him more casually and continue to see him, but I just won't sleep with him, I will keep my options open, and maybe will see other people, too. I don't want to stop seeing him altogether.... and yes, I agree that six weeks is plenty of time to ask about being exclusive, especially since we have been sleeping together, multiple times now, and went away for a weekend together. I don't need us to be all serious all of a sudden, but if I'm going to sleep with him, I certainly don't want him talking online to other women still. I have no interest in pursuing other men right now either.