With your DP veering between "he doesn't even want to anymore" and "he may be watching but not wanking off to it" and "he's only using the one site" and "he'll watch some with you", it's a rather slippery slope. It means you are condoning him doing so, and it's not that big a leap from well, she's happy with me watching some porn, why then shouldn't she be happy with me watching other porn, and him beginning to watch other porn.
Plus, if he has lied to you so far about his use of porn, it is not impossible that he may be lying about what sort of porn he watches/which sites he uses. I mean, on here, we always tell women to be wary when a man who has lied to them says, no, it wasn't, well actually, it was just this, but actually, it was a bit more, but not that ... so I suggest that you keep your eyes open to the possibility that he is not being completely open with you.
You also haven't addressed what made you feel insecure and actually weepy. Was it him watching porn? Was it him watching it without you? Was it just him lying about it? The fact that you make reference to you believing (prior to catching him out) that your sex life was good seems to indicate you believing that his need for porn negates in some shape or form the sexual experiences he has with you. Whether that's to do with him engaging in it without you or engaging in it in the first place is a question only you can answer.
I think my own views on the subject of porn came out loud and clear. Unless you can say in all honesty that the porn you are watching doesn't involve abuse of any sort (a matter that's even harder to verify when it is accessed over the internet, as opposed to a licensed porn shop), then it's possible that, in watching porn with him, no matter how "tame" it seems, that you are condoning or complicit in the possibility of the actors/actresses being forced/coerced into performing.
However, if nothing else, I'm glad that you've reached a compromise that works for you both.