Bisexual or Heterosexual, to stay with you he must stay loyal make that clear to him other wise you'll finish. I wouldn't force him to get off the websites as it could be a compulsive habit, such as one caused by the abuse of heroin.
If he needs it go with him to a relationship counsellor, that will make or break your relationship to put it bluntly. Under no circumstances should you damage your computer or some how prevent him from accessing these types of websites. Yes, conventionally he shouldn't and in my opinion he shouldn't for the very fact he's in a relationship. If you do prevent him however he'll just become secretive and resent you for it - things may get so bitter that you break up on a negative low.
Don't pester him but sit him down and ask him his reasons for being on those websites (honestly don't believe him if he says something like mates did it - I'm sure if it was a prank they'd own up in order to protect their relationships - if he says it go to his friends and ask them, if he truly is and doesnt want them to know the chances are he'll persuade you out of it.
If he's bisexual then thats fine.If he turns out to be gay will that mean the end of your friendship too? Could you bare seeing him with another person, even a man?
He without does love you and doesnt want to see you hurt. It might just be a phrase he never had as a kid ...
Don't do anything life changing during his "troubles", having a child or talking about weddings may just make things worse ... he'll be an emotional wreck.
What I do suggest and obviously you'd have to talk together about this ... you take a break in your relationship, no contact (other than vital stuff like family emergencies). After the two weeks or however long you decide ask him again what he was doing on there is he bi/curious is he just exploring his sexuality? Could it be that he's not happy in himself? Is it because of him not having enough sex?
If he truly wants to continue, reaffirm that you know he loves you, but ask him if he's in love with you ... indeed if he is he wouldnt spend his time on matching agency website things and instead spending time with you goin out or just making your dinner.
If he turns out to be gay, you need to find it in you not to hate him but see you as a friend. If he comes out to you don't tell anyone as this will seriously mess his head up even more.
The joking thing happens with people all the time, its been asked to me and I've asked it in not as many words. My reaction now would obviously for anyone who I've known for years is (non-negative) shock, if they were serious but I'd act unbothered due to the fact if I acted horrified (as conventionally some/most males do) I may infact be sending them back to square one.
The chances are he's bisexual, if he's still got them, his "advertisments" should tell you his sexuality. Ask him about it - don't bug him or harass. If someone kept questioning me and invaded my privacy by installing a key logger for example, about anything not just sexuality, I would want nothing to do with them for their annoying nature.
I sincerely hope my answer has helped, and I wish you both well in the future whether you choose to spend it as a couple or if you decide to go your seperate ways =]
I went through a similar situation (different circumstances) a year ago ...