Thank you everyone for your replies so far. I really appreciate it. Some more context, which may be helpful: I'm 31, he's 38. Aside from the age disparity, there is also a physical one: he's very, very overweight, and I'm average weight. I've never cared about this except in the respect that it does make sex difficult for him sometimes, and gives him a lower libido than me. Throughout this I have always tried to be understanding and accommodating, but regardless I have always been up for trying new things, and am always initiating, being physically affectionate, etc. It was only lately that he started to seem annoyed by me touching him, which he said (after I found out about the online affairs) is because he felt too guilty and ashamed for me to touch him after what he'd done.
As we've had many, many discussions over the past two days to try and get my head around this, we talked about how he engages in these online affairs and what he gets out of them. I had noticed in what I had seen that the women were the only ones to send pictures, not him. All of his sex talk was pretty much identical to the stuff he says to me in bed. So I said, well, what are you getting out of these interactions that you don't get from me? And what it came down to for him (and this felt like the truth, finally) was that these online interactions allow him to engage in sexual activity without the fear or worry of anyone seeing his body. (Keep in mind that I have never said anything but positive things about his body, so this is not a response to any criticism on my part.) None of these women know what he looks like -- the ex-classmate presumably hasn't seen him since high school. To put it quite bluntly, I think even if the opportunity presented itself, I'm not sure how many of these women actually would sleep with him in real life if given the opportunity. Additionally, we both work from home, so it would be really difficult for him to schedule an in-person liaison without me knowing. (All the timelines and everything match up -- when he goes to the grocery store, he comes back quickly with groceries, when he goes to his mom's, he comes back quickly with something she was going to give to me, etc.) (I do of course now wonder if anything happened before I moved in.)
This is one of the reasons why I do actually believe that things never did or never would get physical -- not just because of the fact that all of these women live far away, and not just because of his body shame, but because he's not exactly able to deliver reliably. This is something I thought we had both managed pretty well in our sex life (there are a lot of different ways to have sex, after all), but his self-consciousness around me continues to be an issue.
From our discussions he also presents this as a joyless compulsion -- something that used to give him a thrill but doesn't anymore. Yet he continued to do it, and feel guilty, and do it again. For that reason, more so than the dishonesty, I doubt being able to move on from this, because in my experience such compulsions are difficult to cure. He was sexually abused multiple times as a child, and I wonder if that is factor -- I've asked him to bring it up in his first therapy session, which is a week from yesterday.
Ultimately I guess I'm at war with myself right now while all these emotions are still fresh: one side says get out, this is unacceptable, you can do so much better, there are so many men out there who would never do this to you. The other side, though, already misses him and is grieving for the future we were so excited to build together (which, incidentally, deliberately did not include children -- I was ambivalent about them and he was firm about not wanting them, so kids were never in the picture).
The best part is: only a couple of months ago, my mom did the same thing to my stepdad, to a much lesser degree (only one man), and with more extenuating circumstances (she's bipolar, and after my grandma (her mom) died, she really just lost it for a while there). At the time, I was so stressed and upset about what was happening, because, having a mentally ill mother and being estranged from my equally mentally ill father, my stepdad is one of the few stable influences in my life, and I was terrified of losing him. Throughout this, my boyfriend listened to me, comforted me. And all the while he was doing the same thing behind my back.