He searches his exes often

I need advice on how to talk to him about this. The short version is we're about to move in together, planning to ttc within months. A month ago I innocently came across one of his ex's names from 6+ years ago that cropped up in his search history. I brought it up, he said it was natural to reminisce sometimes. About 2 wks later I mentioned I'm uncomfortable that he's friends with long ago exes on FB. He seemed annoyed & was dismissive. Given his response & our serious plans, I admit I have since looked at his computer's & FB search history. It felt like my heart stopped. He actively follows them, but worse: he searches at least 2 exes a lot, at least fortnightly. I'm disturbed & devastated. Its obsessive, stalkerish behavior! He must have realised as he now deletes his search histories. That's really frightening me about ttc & build a life with him. I'm unsure how to raise it as I went looking. He's otherwise thoughtful, supportive & a great BF to me. But it feels like an emotional affair & I've cried a few times since Sunday. Advice wanted.