[Snupoker]

You can start by not raising the chip-leader's bb with super-marginal hands aka (K-10). Your flop bet seems fine as well as your call of the min-checkraise. However, when you make your flush and the board pairs you have to proceed with EXTREME caution.

Look at this from the big blind's perspective. He is playing from the blind against the other stack at the table that can knock him out of the tournament, so he too is playing warily, but knows he can bluff you off some hands. When you dont re-raise him on the flop, he can safely assume if you are somewhat competent you dont have a big pair, but maybe two big cards or even big hearts.

Back to you as the board pairs the turn and he checks to you. the pot is at 5k, and you bet 2.5k and he min-raises you again. Think about this, is there ANY chance this is a bluff? I dont think so, bc youre gonna call the 2.5k more even with marginal hands. He wants you to commit more chips.

This is the decision point in the hand. Do you call, fold, or raise. Folding, is pretty much out of the question as I would probably even call this min-raise with the naked Ace of hearts. Calling, is an option if youre still unsure of what he has. This will lead to much clearer action on the river, as I cant imagine he tries for 3 check-raises in a row and will lead out for most of his stack. Raising, is essentially all-in (which you choose) and is another valid option.

This is clearly results oriented, but calling seems like the clear play here to his 2ND check-raise on the hand. When he inevitably leads the river, you are again put to the test of what to do. Hands that beat you, 33, 66, 88, 86, any Ax of hearts. What hands would he play like this that you could beat? He's not on a 6 here, as he wouldnt have check-raised the flop. This is where your read of him comes into play.
has he been bluffing excessively, if so this is probably a call all-in on the river. Otherwise, when he bets the river you probably have to fold and grind your way bakc up. I dont know if this made any sense, but I tried how a sensible line of thinking would be and this is what came out.