This is early stage of a tournament, no stats on villain
I'm thinking now that he has every J on his range, so how should i play this hand?

UTG: 101.21 BB
MP: 34.73 BB
HJ: 26.99 BB
CO: 48.9 BB
BTN: 57.32 BB
SB: 56.15 BB
Hero (BB): 34.95 BB

Pre Flop: Hero has 10 10

fold, fold, fold, CO raises to 2.5BB, fold, fold, Hero raises to 8BB, CO calls 5.5BB

Flop: (17.38BB, 2 players) 5 J 8
Hero bets 4.34BB, CO calls 4.34BB

Turn: (27.6BB, 2 players) 9
Hero bets 23.6BB and is all in, CO calls 23.6BB

River: (73.27BB, 2 players) K

CO shows J J

I like your play pre. Your sizing is just above 3x. I usually go 4x when OOP but given the shorter effective stack sizes I think your 3bet size makes sense.

On the flop, I am not sure what the correct strategy is - c-betting small or check and re-evaluate. I think I lean towards the latter. Because if you bet and get called then what are you gonna do on the turn? By checking you protect your checking range. Villain is never folding J or better on this SPR of 1.5. Usually middling hands are better played as checks and not bets.

On the turn, you are turning your hand into a bluff. Because you are unlikely ahead after villain's call. I think it is a marginal decision between jamming and check-calling. I am not sure. It seems close. It is unlikely that the turn will make a fundamental difference in your winrate. But I do not know. Seems close.

Overall, I think check the flop and re-evaluate. It is hard when betting your middling hands because you do not know where you stand.

Thank you for the answer!
Yes I think the check on the flop might be a better option.
I feel like I played the hand blind, it's hard for me to give up this kind of hands.

Would you consider checking the turn to see what villain's action is? If villain had a suited Ace or maybe AQ your bet here gets rid of many hands in villain's range that missed the flop, while letting them keep all the hands that currently beat you, like overpairs, completed straights and sets. If you check, you may get more info from villain about whether they've got something or not.

Check the flop. There's literally no purpose to betting it.

pre is fine, I would check flop as with x1 overcard our hand is only worth 2 streets max so might as well try to take that condensed street now, it keeps in all his worse hands and induces him to bet them which we can easily x/call and re-eval turn

Literally no purpose? How about value and protection?

You're right I shouldn't have used hyperbole. We get protection from some hands but I pref checking.

OK OK, but the turn is gross, I know, I've been there, pretty narrow calling range otf, I honestly think pre is Flat with this many blinds, or just shove pre for variance You ever try free rolling your equity?

I like shoving pre cos it looks like we have AK and we will get called by lower pocket pairs sometimes.

Yeah, jamming pre isn't a terrible idea at all.