Hello Gabinr1,
Sorry for taking that long to evaluate your hand. Don't know why nobody did yet. 
At least I found it. ♦
Flop: Most likely I'd still CBet such a dry board unless I expect the opponent really floating too many boards or being too aggressively. Although according his AF I doubt that.
As played
Turn: Well, that's really ugly while we face such a play. I really doubt that he is Check/Raising as a bluff. Therefore bluffs are already excluded. But I can't exclude 2 pairs from his range here, or do you think he would play any differently 2pairs? I mean he could still even slowplay them.
Obvious that it's likely that he would very often even bet the turn with 2pairs and most likely with strong sets slowplay less. But while we don't even know the opponent, he has a very wide range, doesn't look like a very good player. For that given reason I guess I am also 3betting it.
Board: 6♣K♥9♦ 5♣
Equity Win Tie
UTG 38.51% 38.51% 0.00% { 99, 66, K9s, K6s-K5s, 96s, 87s, 65s, K9o, K6o-K5o, 96o, 87o, 65o }
UTG+1 61.49% 61.49% 0.00% { 5h5s }
But when we face the 4bet it becomes ugly. I mean the guy is pretty passive and even does kinda trapy-line. With 2pairs I'd expect him now even to 4bet bigger, might be scared of any kind of better 2pairs or whatsoever. Therefore it might be towards only strong made hands, unless he doesn't know how to raise it differently. ♦
For that given play-style I'd be even for the crying fold but of course if you even decide to go for the stacks against that kind of guy I doubt it's way off here. He may still be new to poker who doesn't know how raise button works. ♦ Who was just clicking randomly buttons.
Best regards.
