I think this should have been folded pre. As played, it's just a cooler. You beat JJ, TT, QQ, And QJ assuming he's going to be shoving top two here.

16 combos of AK, 14 combos make up QQ-TT, QJs, JTs. I think you have to play it fast like you did, any A, K, 9, or club on the turn can kill your action from hands you beat.

I agree with the two posters above, this is pretty much always a cooler expect against people who cbet very polarized in this spot, meaning, against someone who is going to check back AA, AQ ect it is sort of pointless to check-raise because we're pumping money in from behind. I think its important to understand this distinction and have a general idea how the opposition plays. Knowing he likes to run tripel barrels is not as helpful and if we thought that that's our opponents leak than we should be check-calling instead of check-raising to capitalize on that.
Preflop is fine, folding cannot be an option against someone aggressive OTB.

I think if you want to have a x/r range on this board the best size is to shove. I just don't really see any advantage to making it smaller, maybe someone could give some reasons?

Why dont we lead out ? Cause we will fold out his bluffs ? But is he really gonna bluff a lot on this kind of a flop ? I am not sure but I think it smashes our range better than his.

This board heavily favors villain, we do not have AK, we do not have QQ and we may not even have JJ. Villlain on the other hand has 9 set combos, 16 nut straight combos, possibly K9 and possibly 98. We are also out of position what means we are always going to underperform our equity. If we donk here the top of our range any thinking opponent will understand that fundamentally our game is flawed. This exact spot may not come up all that often, but there are plenty of spots where it is important to protect our ranges and if he thinks they are out of balance and if he is capable he can apply more pressure on our weaker range, making us fold more. Now obviously one can argue that this is never going to happen at lowstakes and while I agree, I still think because we are such a dog against villains range that we should practically never lead out here.

I do not have a good reason why we should not check-raise allin. I'd be interested in that answer too.

I dunno, but when I put AA-KK, AQs, AK, ATo, A9o, KJo, KTo, QJo, A2s-A8s, 86s, 97s, K6s-K9s, Q8s-Q9s {which is my 3bet range on BTN vs CO} and I give us 8s9s and this board, Flopzzila shows me our hand has ~86% equity against that range. What am I doing wrong ?

He has got: 6c sets, 6c two pair, 12c overpair, 7c top pair, 14c FDs, 52c OESD

BTW: You really dont have to worry about balancing your ranges at nl10.

your hand is favorite against his range, but his range crushes your range. I suppose it would be okay to lead out against fun player you are never going to see again, but then again, anyone competent seeing this stuff knows what you are up to. hero has 2k hands on villain and he does not look like a big fun player.

I dunno, but when I put AA-KK, AQs, AK, ATo, A9o, KJo, KTo, QJo, A2s-A8s, 86s, 97s, K6s-K9s, Q8s-Q9s {which is my 3bet range on BTN vs CO} and I give us 8s9s and this board, Flopzzila shows me our hand has ~86% equity against that range.

Use Equilab or Pokerstove and instead of giving us specifically 9s8s give ourself the range that we would call the 3-bet with.
Also, I guess you just forgot to write them down, but I doubt it that your 3-betting range misses QQ-TT.

Depending on what he 3-bets and what you call this board is average to slightly favorable for villain. But being OOP really hurts your EV as we are always underperforming our EQ because our realization is poor and the board is super wet, meaning equities could change drastically depending on what cards come.

because you want to make the most profit with your ranges, not your individual hands. just as a simplification: if you make with your two best hands +10 points, with the next three hands +5 hands, but with the back or your range 0 points you'd be making 35 points. however, if you play your ranges in a way that they support eachother, you may be making +9 with your first two hands, +7 with the next three and +3 with two more, adding up to 45 points.
now this illustration is flawed on many levels but i hope it brings across the point.

well because if you have a general idea if a board is good for you or your opponent you have some idea of how to play your range/hands.
in this case, since this board favors your villain you do not want to lead out, you want to check-call to protect your range and by doing so you are seeing more SDs and winning more money

How am I protecting my range by check-calling ? What does "protecting" actually means (in this case to make it more simple) ?

In this context "protecting" means that when you check-call, near your weaker hands like KQ, KJ...here you'll have strong hands so your opponent can't just go overbet or 2/3barrel randomly (here like 6h5h) vs you and make profit cause your check-calling range sucks and you will fold always (later streets).
Although this is certainly not a concern at this stake in this situation.