The Solver Logic

A flop check-back from the in-position caller in a 3-bet pot reveals a very weak, capped range — they'd bet most strong hands, so the check leaves them with air and underpairs. That lets the out-of-position player attack the turn with a large barrel (around pot, setting up an all-in), leading a wide range on the cards that favour it. The check-back is the trigger to get aggressive, not to slow down.