Dont want to know who the villain was but you and I play in these where I miss a few a week and you miss a few a week but the point is that its the same 50 players or so meaning you should have a feeling about what villain does or doesnt do. The bet on the flop is strange due to their stack size and also over betting the pot but I could rattle off names we play against (of course I wont here) that if they made this bet it would not freak me out that much since they pay high variance and its how they play where others could make this play and I would be like, what the hell is going on here. So only you should know how this sizing makes you feel from this villain. However, in a vacuum without knowing who it was I find the bet sizing odd and my thinking would go along the lines of...
1. Villain is never folding this hand no matter what
2. Would villain bet their sets and two pairs this way off this stack? My answer would be no, they would bet flop to where they are jamming under pot any turn even if the flush card were to come out
3. Would villain do this as a
bluff or with a hand that is now weaker or vulnerable? My thinking would be yes they could since we are already in the money and now the pay jumps in 2023 being changed and only $5 more to 2nd and only first has the decent jump. With knowing that villain could easily being playing to win and sees a spot where they could get you to fold some smaller Ax.
With all that, and your stack size, I would just call as you did (depending on the villain of course) and be a little uneasy about it but there is enough there that I think doesnt make sense for me to attempt to sniff this out. No reason to ever raise the flop as we know villain is going to fire turn and is never folding here so if we are ahead might as well let them completely tighten the rope. However, when we call we are never folding either so from that perspective I guess it is fine to get in with a raise but I would not want to risk it given maybe they fold if we jam if they are on pure air (I know I said they werent folding, but we risk it if we jam so let them finish off the hanging if we are ahead).
Then on any turn I expect villain to fire whats left and you just call as you did. Yes its bad luck that they got the K on the river but you did have the fortune (even though it winds up costing you) of hitting the ace when pre flop you were way behind.
You ask should villain fire turn... I think based on how they played the hand (which I disagree with strongly) they kind of have to (especially with the no pay jump to 2nd now and they already have half in by turn) but they should not have put themselves in that spot to have to go on the turn.