raise more preflop, 4xbb+1/limper = $1 to go. flop action is fine. Turn I bet 2/3 pot again, an overbet is asking worse hands to fold and better hands (made straight) to call. I just call his raise, I'm not in a hurry to push as that turn card completed the straight draw. Check/call a reasonable river, the queen completes KT str8 which isn't a likely holding on a villain unless you have a read on him being an aggressive idiot. Don't bet river because it pot commits you when he raises with the nuts.

Edit: I didn't even notice the diamond draw, but I'm still not pushing, a pot sized bet is enough to make calling incrrect

Edit2: and after further thought, you can't fold the river after calling that minraise on the turn, a push is only for half the pot. Pushing the turn seems like a better option now.