Welcome to the forum. I assume, this is a cash game hand, since there is no ante. Please post in cash game hand analysis next time. You can read the posting guidelines to see, which topics belong where.
Preflop
No problem with 3-betting against a CO open.
Flop
I guess, some argument can be made, that we are "range betting" on this dry A high board, but if we ever take a hand, where we just give up, this one is a good candidate, since we pretty much missed completely. We dont even have a BDFD or anything to give us
equity, if for instance we are behind to top pair.
Turn
2c does not help us in any way, and I am pretty much just giving up now. Check and fold to any aggression.
River
The issue with this
bluff is, that its difficult for you to represent a real hand, that you would play this way. If for instance you had a hand like AK or AQ, which you can credibly represent after 3-betting pre, you would not have checked the turn and then bombed the river, when the BDFD completed. Instead you would have bet the turn and checked the scary river with intention to check-call most bets from him. Most people would also fire the turn, if they picked up a flushdraw. If for instance you had KQ of clubs instead of KQ offsuit, this would have been a perfect turn card to barrel.
So you are kind of saying, you took a tricky line with a boat or rivered it with 77, and now you are hoping, that he made a flush at the end or will hero call you with a weak top pair or a hand like TT-JJ. You are repping very thin, so if the opponent can hand read, he is very likely to do exactly that. I dont think, you should ever be betting this river after checking turn. Just check your entire range and then go for a check-raise, if you rivered a boat with 77 or slowplayed 99 or A2s on the turn.
His raise is not representing a lot of hands either, since what I wrote about you above pretty much goes for him as well, although he might be somewhat more likely to check behind on the turn with a BDFD, especially if its a hand like AT or AJ of clubs, which also has showdown value. But would a flush even raise the river on a paired board? Thats also up for debate.
So he is also kind of saying, that he has a slowplayed boat or rivered it with 77, and now he wants to get maximum value. He is also repping pretty thin, but at the same time he could be turning a made hand like J9s or T9s into a bluff, so we dont even beat all his bluffs. So pretty easy fold at the end, but I think, the river bet and maybe even the flop bet could have been saved. When we are at the rock bottom of our range, its always ok to just give up, especially out of position.