Against these types of players you should be raising over their limp by more than 4x. 4x is normally fine against players that limp fold at least somewhat often but against players that will limp call then you should be squeezing a few more BB of value from them pre flop and going bigger, either 5x or 6x.
As played on the flop my alarm would already be going off if they are the type of player that you write they are. I dont think very often if ever they will be leading into me after I raise pre and they lead into us for 83% of pot. I would never put them on the hand that they have but I would already be thinking possible set and knowing that they have something whether it is an overpair to the board, a set, draw, etc. I would call this flop bet but again, I am not loving this even with QQ.
The turn is a good and bad card. Its good since it reduces set of 5s but it also helps the A5 get there which is a hand they could have here since people really love A5 suited for some reason (I get why its liked just dont get why its loved). I noticed the sizing here sets up a 3/4th pot river shove quite nicely too, not sure if villain was trying to do that or just stumbled into it. I would be calling here hoping the villain is on 88-JJ but again I am not feeling good about this.
The river brings the King which I take as a good card because to me it should make the villain really define their hand. This would be a villain dependent here as are they the type of player that would continue to bet with JJ-88 here with an overcard hitting the board? Not sure what the answer to that is but if I felt they would hold up here and not bet those hands on the river then the river shove is a fold to me. If you think they continue to go with smaller pocket pairs then it gets real tough. My gut here would tell me in game to fold since they are going 3 streets, all big sizings against a pre flop raiser. Maybe they are a maniac and would do this but I feel like they have something here they are confident in. My initial guess would have been a set since they would probably play it the same way. Tough spot to be in with an overpair but I fold the river here, its nitty but I fold. You also mention that this player has limped before with KK so those types of hands could be there as well when normally without a raise we would think they wouldn't be. Tough hand for sure
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