There is no way you should lay down at any stage. I think you played this hand perfectly and the check-raise on the turn is the best play regardless what falls. You really don't want him laying down AKxx etc here, which will presumably happen if you CR the flop or lead the turn. I think letting him hang himself is fine.
I probably bet the flop if the stacks are shallower but really I like your play - I think you want this hand all-in and you want to do it in such a way that he'll put in with hands that are a long way behind. I think you can discount the potential damage of him having AA against the far greater benefits of him putting in with a range of other hands.
Nothing to add to that, really - given your read I think your play was fine. The only problems I can see are an ace hitting the turn (makes life hard OOP) or if you don't have the flush draw as back-up. That flush draw makes it so much easier to ignore the possible damage of getting in against AA - getting in as a 35:65 underdog (vs AA) is bad, but getting in as a 95:5 underdog (vs AA without the flush) is a disaster.
You are possibly playing slightly scared given the tone of your post, but I don't think that's a bad thing - I often actually find that I play better poker above my comfort level because the games tend to be more aggro and I tighten up and make fewer exploitable marginal "moves", instead making solid plays as I feel you did here.