Hi,
I see no reason to check the flop without reads, the fish will show up enough with random broadways that whiffed this flop to warrant you not giving up right away. If you know better and think CO is a reg, then he always has something like QQ+ for coldcalling such a strong-looking 3-bet, meaning it's no use throwing money at him on that board.
On the turn if you're not going to check/fold, just shove it in his face. Once you check and he bets so big, you have no fold equity whatsoever, which means you're choosing to go broke as a likely 2:1 dog or close to it. It just has all the drawbacks of a turn shove, with none of the benefits, so it's simply a dominated strategy in that spot.
Hope it helps.