Hand 1: I hate the turn min-raise but I'm not folding KK yet. What to do on the river shove with my boat?

$0.1/$0.25 No Limit Holdem
2 players
Converted at

Stacks:
Hero ($31.30)
BB ($22.20)

Pre-flop: ($0.35, 2 players) Hero is BTN [Kh]
Hero raises to $1, BB calls $0.75

Flop: [4c][4h] ($2, 2 players)
BB checks, Hero bets $1.25, BB calls $1.25

Turn: ($4.5, 2 players)
BB checks, Hero bets $3, BB raises to $6, Hero calls $3

River: ($16.5, 2 players)
BB goes all-in $13.95, Hero ??

Hand 2: What do you do on this turn? If I am considering committing myself fully to this pot then I should probably be betting at least $9 on that turn and calling a shove, right? After UTG shoved I felt I was behind but getting nearly 4:1 on my money I called.

FTR Hand History Converter Output (intended for copying and pasting into poker forums!):
Full Tilt No-Limit Hold'em, $0.25 BB (6 handed) Converter Tool from (Format: FlopTurnRiver Cards)

saw flop|saw showdown

BB ($9.80)
UTG ($20.25)
Hero ($30)
CO ($28.75)
Button ($12.60)
SB ($18.05)

Preflop: Hero is MP with , .
UTG raises to $0.85, Hero calls $0.85, CO calls $0.85, Button calls $0.85, 2 folds.

Flop: ($3.75) , , (4 players)
UTG checks, Hero bets $2.5, CO folds, Button calls $2.50, UTG calls $2.50.

Turn: ($11.25) (3 players)
UTG checks, Hero bets $6.5, Button raises to $9.25 (All-In), UTG raises to $16.9 (All-In), Hero calls $10.40.

that was what i noticed as well. you could/should bet those flops bigger. JAT