I would say to confront him about it, not aggressively of course. Try to assume possible reasons as to why he is on on-line dating sites before you do talk to him, this way, you are less inclined to accept any excuse he might use, and are better able to judge his sincerity/honesty.
From personal experience, I know my boyfriend, after we would have a great bonding weekend, would re-experience the insecurities that are natural to a relationship, and briefly become ambivalent about us. It means progression. Looking through on-line dating sites may just be a harmless way for your boyfriend to cope with initial onsets of insecurity, upon passing, he accepts the progression of your relationship, and you two are stronger.
And Who knows, maybe he is checking these on-line dating sites to make sure You aren’t on there. My bf used to go on the craigslist personals first to make sure I didn’t post anything and second to see what kind of girls were out there, not to date them, more out of curiosity. Guys just have this innate curiosity to look- at porn, at other girls, whatever. It’s kind of stupid, but I’d say most of the time they are doing it as brainless activity. (Guys don’t think sometimes!)
IDK what it might be for your case, and talking to him is the only way of finding out. As you can see, the looking at online dating sites can appear as harmless brainless activity, but on the one hand, it could be a well-conceived intentional act. So, Make sure you understand his Intention, his intention is key. If he states his case and doesn’t explain himself well, make him convince you. You shouldn’t sacrifice your peace of mind and well being for anything/anyone. A healthy relationship should be able to nurture you, and be a provider of well being. If you two are in a healthy relationship, he would explain himself and not mind doing it. If he gets defensive and snappy, you know his concern is to protect himself instead of reassuring you, and that is selfish! Good luck!