Should I dump him or let him stay?

I've been dating this guy I've known for 3 years, but we've only been officially dating for 4 months. He gives me his iTouch over the weekend to keep me entertained while he was away at a tournament. I wanted to check my email, so I clicked his mail app. It was already logged into his, and I guess the curiosity got the best of me, and I looked in his inbox, nothing unusual, until I saw someone without a person's name, but it was very weird. The title of the email was "Happy Valentines Day babe! <3" So I clicked it, and I saw this person saying that she loves him & misses him. & she attached a video of her just carressing her breasts. Then there's no more of those messages in his inbox, but when I check his sent box ( I know, I'm at fault here for creeping, and I apologize ) there's more conversations between them, and there are more sexual videos and porn-like things. I know he had a porn addiction, and I didn't really mind. Well, I sort of did, because I felt like I wasn't good enough for him or was satisfying him enough that he'd have to go to another girl to find that satisfaction. But the fact that they were talking back and forth and calling each other babe, I couldn't believe my eyes. I double, triple, and quadruple checked he was writing these things. Yes, because one of the videos was addressed to him, using his name. They started talking in September, and they kept talking through November, AFTER we started dating. He was calling her babe and sending her videos of who knows what. It gets worse. I confront him about it, and he makes up this excuse that he was offered a gift card that he had to give his email, and he got all this porn as spam. But I said if it was spam, why are you replying and the messages end up in your sent box? He started making me feel guilty and turning the tables on me. I had just been crying because my mom had been verbally abusing me in the car about my weight, and I had cried twice. He asked me if I trusted him, and I said, "Yes, until today." Because I knew the truth. He didn't know. & what's shady about it is, that as I was talking to him, I noticed he moved the messages from her into his trash box. I don't know what to think of him. We made up today, with me crying and apologizing. My friends have been telling me to drop him, and I get all confident and pumped to dump him, but when I see him, I get weak in the knees and just make up with him. He says all these things that sound so genuine, but I know that my trust in him now is weak. I had already been feeling down about our relationship this week, and this situation just made it worse. We've been through so much, and something inside me still wants him in my life and doesn't want to let him go. Maybe this girl is just on the side, but am I willing to put up with that? I'm going to demand that he stop talking to her, but he'll just deny he's talking to anyone. I love him, but I know he's not treating me right, but at the same time, he's saying how much he loves me still. What should I do?