I checked my on/off BF's facebook. I suspected he cheated and I was proven right. Was I right to do it?

[Stranded]

I've been dating this guy on and off for four years. The problem is that he's never been able to fully commit to me. I've made all kinds of sacrifices to be with him. Our relationship a secret since he's divorced and has kids, so he's afraid of his relatives might think about us. We've been through a lot together, but mostly it's me tending to his needs. It was a first same sex relationship for both, so he was "straight" until he met me but he's never stopped looking at women. We rarely had intimacy -only 3 times last year- and it wasn't to my satisfaction.

He said he still likes women and I caught him checking them out and texting female friends, but he swears it's innocent, though he did admit that he hooked up with a girl while we were "on a break". I still felt betrayed and since then I've admitted that I haven't been able to fully trust him.

Because of this I've distanced myself from him several times, and told him I don't want to see him again, but a few weeks will go by and he always finds a way to reel me back in, promising it'll all be different this time around. I've met others who have expressed interest in getting to know me better and go out with me but I've ended up not taking on their offers because I was committed to make it work with him.

I've become unhappy, frustrated and depressed. I feel like I've wasted a lot of time. Recently I told him that I felt he had never been honest with me, we both deserved to be happy, so I asked him to tell me the truth, and we could break up and remain friends. He denied ever cheating on me, and said I was the only one he loved and said he didn't want to leave me. He said made up his mind about wanting to be with me, and he's made many mistakes in the past and didn't want to lose me. I kept asking me what he means by "mistake" but he didn't go into details.

The other day he checked his Facebook account using my tablet and forgot that the password was stored. I ended up checking his account and went through every message from one year onwards and I discovered he had in fact been with different women and possibly other men during the time we've been together, especially last year.

I didn't know how to confront him about this, so I called him up and told him I loved him deeply and meant the world to me. I felt like crying so I told him I had to go and hung up. Hours later I texted him and said that he had hurt me in unimaginable ways, so I didn't want to hear from him again and he might as well pretend that I was dead to him.

We haven't spoken since. He called me non-stop the next day but it seems he finally got the message. I don't know whether I should confront him or not. I know checking someone else's FB account is morally questionable but the thing is, I would've never found out how he's treated me had I not taken a chance to check out his account. Was I right to do it?