Help. Should I be worried about cheating?

Many years ago I was in a horrible relationship with someone very violent and controlling who also cheated on me, which led me to become very paranoid that the same thing would happen again. Years later I am now with someone a million times better who treats me with respect, we are married and expecting first baby. I do however have trust issues that will never go away and I once checked his Facebook to find that he had been viewing the profiles of a couple of women he worked with, repeatedly and for months on end. We talked about it and he said it was nothing and deleted the app from his phone etc. He doesn't really use it and made it clear he said it was evil. In the last few months I have been getting some weird vibes off him again about women at work, I trust him but I also have a sixth sense when it comes to these things and I thought I better investigate. He has deleted the app but is still going on the FB website via his browser so I can see all the history. He deletes the activity log search on FB each time but not the history! Duh. Turns out he has been looking up one specific woman at work for the last couple of months, they are not friends and there are no messages but the frequency of him viewing her profile concerns me. I thought first of all that perhaps he was just curious and like we all do taking a quick look However today I have discovered that he has been viewing photos of her in a bikini. She is skinny but average looking so I don't think he is just having a perv at a young bit of stuff. I am really concerned now that he has developed feelings for her both sexual and emotional I just don't think this is normal. We are otherwise very happy and he is excited about being a dad I am just so upset because I hate that he is thinking about someone else. What shall I do?