I am posting this hand for LiarsDice. There are two points I want to question
1) Is the river bet good?
2) Is the turn bet good?
1) Is the river bet good?
I think emphatically yes. If we check, we are not going to see a bluff often enough. Hands better than ours (a four) will bet and hands worse than ours will check. If we bet, we will be getting called by a middle pair. Therefore, betting has more value than checking.
2) Is the turn bet good?
In my mind, I prefer to check this turn instead of betting. Betting the turn sets us up to play an overpair on a four-straight board for stacks 75bb deep, which just sounds bad in my mind. Additionally, we tend to bet a turn in this spot if we wish to charge a draw (LiarsDice's reasoning). However, given that this is heads-up poker, ranges are very wide and players tend to have draws less often than we would expect. Additionally, for checking the turn to cost us money, he has to both have a draw and hit his draw (which is 8% for a gutshot and 16% for an 8-outer). Since these draws almost never come in, and he almost never has a draw, charging draws has very little value. Pot control takes precidence.
Perhaps, though, we're both just very good players and we're elaborating on a decision that's too marginal to be of importance. Discuss.
I think we should go bigger on the flop because the hands that are going to peel a card against us have fairly good implied odds. For example, if he decides to peel a card here with KQ or 65hh and he improves, we will end up paying at LEAST 1 more street if not 2. I think that this flop bet is smaller than optimal.
I think the turn is ok against a thinking player but awful against a fish. A thinking player could recognize that your 3bet range doesn't hit this board much so he might expect you to have 2 overs like AK, but a fish is usually just going to be like "ok, I don't have a 4 so this is an easy fold."
I think that the river is also very dependent on the villain. I don't think that a complete fish is ever calling your shove here with worse because the bet/bet/bet line looks strong to them and they probably won't be doing enough hand reading to call you down with a worse pair.
Given that he got looked up by 6X i think his line was probably ok against this villain, but I think that against most randoms this would be a big spew. It would help a lot to give a description of what you know about the villain along with the hand history. If you don't know anything about the villain then that would be helpful to mention as well.