Quick back story, I have a cash game background but I'm switching over to tournaments. Played a lot of tourneys back in 2015 but haven't played much since. I still find myself thinking like a cash player but I'm trying to adjust.

Villian is an unknown

Blinds are 40/80, Villian is in MP with 9k. I'm in SB with 10k.

Villain opens for 240. Folds to me. I raise to 880 with QsQc. Villain calls.

Flop is T22r. I lead for 640 into a pot of 1880. Villian calls.
(My cash game thinking says this is a standard range c-bet for 1/3 sizing in cash but is it the correct play for tournaments? )

Turn is a 3d putting a fd on the board. I lead for 1840 into a pot of 3120. Villain calls. (I decide to size up OTT to charge draws and put pressure on his Ax that floated and medium PPs)

River is a 5s. Board reads T2235. My stack is about 6.5k. Villian is at 5.5k. I bet 3500. Villain shoves. I call.

Never folding just unlucky we are beat.

I think flop sizing is fine in a vacuum but betting a little more here will make it easier to gii comfortably on the river. As played I would still shove the river for more value from Tx JJ -
There is not much beating us so assuming you did lose its just a cooler.

You can bet more OTF. He still can call with many hands. Shove OTR. In the tournaments you play for double up, not like in the cash games (for blinds). I mean in the cash games, if you double up this is just "profit". In MTT this is not "2x profit". The big stack is advantage. You can find another good spot after this. This 3k chips remaining already is not 2x, but 4x. And 8x, 16x . Good spot to put all your chips, then do it. Don't do NAI bets OTR. With this SPR...Think about AI OTT, OTR. Use more suitable sizes for your "target". OTT often is very profitable to go AI, than NAI bet OTT, shove OTR. Also with check-raise OTT. You can't do that here. Just use bigger size OTF. Not so big ofc. Bet OTT, shove OTR.

Think like that....You see a cash table with brutal fishes. All of them have 200bb. You have 100bb, the max buy in for the table. Then you will go AI postflop with some strong hand, correct!? In the MTT there is another factor. ICM...If you have bigger stack than the other players, in the late stages, you "moves" will be more EV.

SOrry for the bad English...