On that board, betting AK is a value bet against bottomset's likely rage. Checking is foolhardy. Checking the turn is not the best of ideas, either. I don't want to give a free card, since he's almost certainly drawing live against me. If he has a hand he'll fold to a turn c/r, I'm winning anyway. Since I capped preflop, bottomset is putting me on a PP or cards that didn't connect with this flop. He's very unlikely to fold any pair. Ugh. And then you want me to 3bet that turn w/ A high, to "find out where I stand?" I'd much rather get to showdown than find out I'm beat in this case. I suggest you read
this classic post by NPA.