Read on the villain: he's a calling station. Called me down to showdown on several pots beforehand.

PokerStars No-Limit Hold'em, $0.05 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG ($4)
UTG+1 ($6.33)
MP1 ($5.52)
MP2 ($2.65)
CO ($12.79)
Button ($11.56)
Hero (SB) ($5.80)
BB ($6.49)

Preflop: Hero is SB with A, K
4 folds, CO raises to $0.10, 1 fold, Hero raises to $0.40, BB calls $0.35, CO calls $0.30

Flop: ($1.20) 5, 9, 8 (3 players)
Hero checks, BB bets $0.20, 1 fold, Hero calls $0.20

Turn: ($1.60) 8 (2 players)
Hero checks, BB bets $0.20, Hero calls $0.20

River: ($2) 10 (2 players)
Hero checks, BB bets $0.20

Total pot: $2

I was out of position on a missed flop with two players still in. I always get stuck here. Thought about c-betting but knew it would be a waste with a calling station in the hand and I have nothing. Tricky part for me was he was giving me good pot odds to keep calling instead of re-raising. But I would be re-raising with nothing against a calling station. Should I have made the cheap calls or dumped it at the turn?