NL30 KK overpair optimales betsize flop/turn?

[Wi11i]

villain runt 54/17 nach 39 hands und hatn nick den HM mit papa abkürzt, also imho schon im vornherein verloren.

Hero (BTN): $40.15
SB: $30.45
BB: $30.91
UTG: $55.68
papa: $44.88
CO: $30.00

Pre Flop: ($0.45) Hero is BTN with K K
2 folds, papa raises to $0.60, Hero raises to $2.25, 2 folds, papa calls $1.65

Flop: ($4.95) T 8 5 (2 players)
papa bets $2.47, Hero raises to $10.17, papa calls $7.70

Turn: ($25.29) 5 (2 players)
papa checks...