NL 100 - Bet sizing problem with under-full house

[YKMM]

I have $69.75 left on the turn. How do I play optimally here? Villain's min-raise annoyed me considerably because although it is likely to be a ten, he still not pot committed if I shove. Does shoving give away my hand here? Villain is 20/9/2 in a 300 hands, no other history.

PokerStars No-Limit Hold'em, $1.00 BB (7 handed) Hand History converter Courtesy of PokerZion.com

Button ($26.35)
SB ($132.70)
BB ($40)
UTG ($111.90)
MP1 ($101.35)
Hero ($97.25)
CO ($128.50)

Preflop: Hero is MP2 with 2[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/spade.gif[/img].
<font color="#666666">1 fold</font>, MP1 calls $1, Hero calls $1, CO calls $1, <font color="#666666">1 fold</font>, SB completes, BB checks.

Flop: ($5) T[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(5 players)</font>
SB checks, BB checks, MP1 checks, <font color="#CC3333">Hero bets $4.5</font>, CO calls $4.50, SB folds, BB folds, MP1 folds.

Turn: ($14) 6[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $11</font>, <font color="#CC3333">CO raises to $22</font>, <font color="#CC3333">Hero ....</font>

[AlexB182]

I'd three bet AI. Mostly he has a T here and won't be able to lay it down anyway and you can not give him correct odds to hit his kicker by just calling here.
Plus if he has you beat with a miracle hand like T6,T2 or 66, you won't get away from your hand anyway...

[CallMeJohn]

Push. I doubt he is folding any T.

If your plan is to call and value bet river, you run the risk of him only calling and you won't get all his money. If your plan was to push the river, just do it now.

[YKMM]

Yup, I pushed, villain used his entire timebank and unfortunately folded.