A cooler would be if you had QQ vs KK. Your 66 is not a cooler. Your 66 was a reasonable raise into an unopened pot on the button. When villain re-raises you — even though you have raised button three times in a row — even if he is doing so light he still either has you dominated (higher pair) or you are flipping (two overcards). I suppose you can just call and see if you hit a set or if the flop is devoid of broadway cards you can decide how you want to proceed post flop. The four bet is a case where you have turned your hand into a bluff. I think four betting with 66 is way too aggressive. And when villain five bets/jams it is absolutely a fold for you. There is now a flashing neon sign over his head that says kings or aces (I don’t see him taking this line with AK). You say he is a competent player so I don’t see him spazzing out with a five-bet jam as a stone cold punt, and even if that is the case you still aren’t in ideal shape against whatever it is you think he has.

About the only situation where I could remotely make the argument for going to war like you did was the situation I saw the other night during Killingbird’s twitch stream. There was a player at his table who was literally raising 100% of hands whether he had a hand (rarely) or not (usually). This player had a huge stack because he kept sucking out against better hands. I think Killingbird got it in good preflop with something like KJ, which against any other player would have been a fold but against this player figured to be way ahead. Killingbird was in fact way in front of villain, but villain binked the flop (or maybe the turn) and won the hand. The point was, I think your opponent would have had to be this kind of a lunatic for it to make sense for you to four-bet raise and five-bet call an all-in with your pair of sixes.