How to extract from flopped trips?

[ghostbeef]

Poker Stars - No Limit Hold'em Cash Game - $1/$2 Blinds - 7 Players - (LegoPoker Hand History Converter)

Hero (SB): $112.80
BB: $91.15
UTG: $46.45
UTG+1: $204.50
MP: $230.65
CO: $115.00
BTN: $203.60

Reads: <font color="blue">Villian is 15/9/5.0 over 300 hands with setmining tendencies</font>

Preflop: Hero is dealt A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/diamond.gif[/img] (7 Players)
4 folds, <font color="red">BTN raises to $8.00</font>, Hero calls $7.00, BB folds

Flop: ($18) K[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img] (2 Players)
Hero checks, <font color="red">BTN bets $10.00</font>, Hero calls $10.00

Turn: ($38) 7[img]/images/graemlins/club.gif[/img] (2 Players)
Hero checks, <font color="red">BTN bets $16.00</font>, <font color="red">Hero raises to $32.00</font>, BTN calls $16.00

River: ($102) 3[img]/images/graemlins/club.gif[/img] (2 Players)
<font color="red">Hero bets $40.00</font>, BTN folds

Pot Size: $142.00 ($3 Rake)

Preflop my plan was to let villian hit TP and let him do all the postflop work. I'll admit I have some FPS in my game. How do you extract maximum from this line? My turn minraise was to feel out if he had the 4th K with a weak kicker and/or how aggressive he was going to play. Should I try $50 on the turn and risk a fold? I think in hindsight I could have made a smaller valuebet on river due to him just calling.