I'm glad it has worked out and all is well, but I got to say I'm horrified by the general acceptance by posters that your snooping and monitoring of a loved ones private material is alright. I would be hurt incredibly deeply if I ever found my dp looking at stuff that I have clearly indicated I wish to keep private, and going through my private browser history would be as devastating as finding them reading my diary.
To me there is no greater red flag than someone who think that being in a relationship means you forfeit your right to privacy. I've been with people who've insisted that their trust must be earned by emptying out my pockets and laying bare my life for their inspection whenever they ask. I felt infantilised, harassed, stifled and oppressed to such an extent that it simply couldn't work after that. And that's what you're doing, only if anything it's worse because you're going behind his back.
His being suddenly very physically affectionate may mean something bad is going on with him, or that something good is going on with him, or it might mean nothing at all. Finding out can only be achieved by talking to him about it. But it's a huge, unreasonable leap to use it to justify putting him in the "under suspicion" category with the suspension of his privacy rights that goes with it (in your book).
Instincts will not always be right, that's simply not true. Everyone's guided by their instincts to a large extent but they're completely fallible (especially on personal, emotional subjects), On some occasions they will be entirely wrong.
There are any number of innocent sites he might prefer to keep his visiting private, he might have a medical thing, he might want to discuss something life/relationship issues in private with someone, he might be researching a hobby/subject that he feels slightly embarrassed about and does not want to share with you at this point, it could be anything.
But he owes you no explanation for his private browsing if he doesn't want to give you one. His life is his business, just like yours is yours. You're there by invitation, you don't get to poke around where he doesn't want you going like you own the place. Sorry if this sounds unfriendly, and I wish I could express myself more gracefully, but I just find this attitude so so wrong.
To trust someone is to take a leap of faith in them. It unavoidably necessitates a loss of control, and leaving yourself vulnerable. But you're never forced to trust anyone, and merely wanting to trust someone but not quite being sure you do (as seems the case here) doesn't justify snooping. It's something you feel towards someone or you don't and can only be built through personal intimacy and impression over time. Proving it is impossible, and attempts to do so are massively destructive towards the chances of romance and happiness in a relationship.
Sorry for ranting at you, any anger I feel here is towards the way the world is trending generally and not directed at you personally at all, I know individual snooping is hardly crime of the century, what I find so chilling is how it's becoming the norm. Anyway, wish you all the best. :)