This hand is a great example of the power of position being even more important the deeper we get. At 100BB I'm fine with raising this pre, fine with calling too. But when we are this deep, we'll probably be in a guessing game for more BB than our hand can stand.
The problem with this flop, as great as it looks for us, is that we are pretty well capped at 1 pair hands. Most of us don't routinely 3! from the blinds with 66 or worse, or 87s and below. V prob knows this, but he's uncapped since 160BB deep he's never folding anything playable, and he can put so much pressure on us. His range is from air to the stone cold nuts with supernuts redraw, with every possibility in between. We're basically screwed here, and a competent opponent knows there is nothing we can do about it (short of shoving the turn which could be soooo spewtastic).
There's a better than 0% chance I'd check back AA oop here, so doing the same with 77 (which has a sneaky oesd) is perfectly fine in my book. (I'd be more inclined to bet flop with KK-99, which are vunerable to overcards and lack the oesd.)
I would chalk this hand up to a lesson in OOP deep stack play, don't be too hard on yourself that it didn't turn out well.