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>