200/400 NL - Overbet = Nuts?

[Dire]

Hand 1: of course you would not check behind AK/AQ or a 7. On the same note, you also wouldn't typically overbet shove the pot for more than a buyin when looking for value. Don't forget to not only consider his range, but also what sort of range we are representing.

Hand 2: you are failing to understand the point of not shoving here. There are basically no hands that call a second barrel, but fold to a shove. Given the board texture, villain likely either has an ace or some pocket pair or nothing. He's stacking off with aces, and he's folding pocket pairs/air to a second barrel.

The point of not shoving is to allow your opponent to make a huge mistake. If he has a hand like AQ that he's willing to stack off with that just calls (instead of shoving) then we have induced a huge mistake. Since we save a quarter of a buyin (or more) when we don't hit, but we still earn the same when we do hit.