I mean, replace reddit with IG, video games or porn. It would probably bother you equally, regardless of the medium.
My guess is that he posts a lot on reddit, and he's checking to see if he has any red notifications. This is what social media aims to do....to get you to constantly check the app and froth at the mouth over notifications.
Should I be worried? Should I look through his common Reddit threads…?
Not sure about that. He could just be posting to video game threads. If you think he's talking to girls through reddit....what indicators would suggest that? Reddit can be used for stuff like that, but usually not.
Why dont you just casually bring up that you're interested in reddit, and wondering what subs he checks out? Dont make it like a "So....why are you on reddit so much" type of negative conversation.