Interestingly, as I originally thought this thread was going to be about objections about fashion choices, it would appear you already have some skill in gently bringing subjects into the open.

That said.. I personally would not suggest using the web history as a starting point, as exposing that knowledge could put what trust you enjoy in a precarious position from which it might not potentially recover.

However, as far as clarity about your future goes, you really just have to ask yourself: can the love you have override whatever unexpressed genuine and nonviolent elements of your spouse's personality and person might emerge? If yes, just keep letting him know that you are a safe place to land, and that there's nothing you'd let separate you. If you think not, just be extremely sure before committing to a "final answer" -- but I would still highly recommend in that case being a soft place for him to land while extending the very best variety of your friendship that you can. Love really can conquer all, in ways that not everyone can always understand.

Of course that's just based on my own individual experience and outlook, which has been the result of having likewise shared a marriage with someone who continued to discover elements of themselves that needed to be expressed long after we first came together. I hope you find peace with this process, and healthy personal growth whatever your journey.