Break things off?

So I met this guy on tinder and we’ve been going on dates/hanging out for a month and a half. From the very beginning he said when he started talking to me he stopped checking tinder. And then said he had deleted it. I never asked him to do either of those things he volunteered it himself. One of the first things he’d also said to me that he was looking for a relationship and that he was tired of hookups. So after a couple of weeks talking to him out of respect I didn’t talk to any other guys (and my tinder was already deleted). The other day I was at his house and I swear he had tinder messages open...while I was sitting right next to him. I didn’t get 100% clear view of the screen. But at the very top middle of the screen there looked to be a red icon (like the messages symbol on your tinder). Circles of pictures across the top (like your matches). And then what looked like messages with the circle of their profile pic on the left...and I can’t think of a single app that would look like that... I know we never said we’re bf/gf or anything. But he’d made it seem like we were heading there and that we were only talking to each other. He’d mentioned me meeting his family a couple times...which he said he only would do with a girl he was serious about. So now I’m like?? Do I even bother anymore??