Flush on board - call a push with 3rd nuts?

I know these are rediculously low stakes - but I think the principle still holds. I can't say I have a read on villain, but my memory if him is he seems fishy. He certainly hasn't done anything this aggressive since I've been at the table (4+ orbits.)

Was I stupid to bet on the turn and river? Is his stacking off just trying to push me off the hand, or does he have the ace?

PokerStars No-Limit Hold'em, $0.02 BB (9 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP1 ($3.91)
MP2 ($2.15)
MP3 ($0.84)
CO ($1.51)
Button ($4.21)
SB ($1.11)
BB ($2.18)
UTG ($1.92)
Hero ($6.06)

Preflop: Hero is UTG+1 with Thttp://www.flopturnriver.com/phpBB2/...iles/heart.gif, Jhttp://www.flopturnriver.com/phpBB2/...iles/spade.gif.
1 fold, Hero calls $0.02, 4 folds, Button calls $0.02, 1 fold, BB checks.

Flop: ($0.07) 7http://www.flopturnriver.com/phpBB2/...iles/heart.gif, Khttp://www.flopturnriver.com/phpBB2/...iles/heart.gif, 8http://www.flopturnriver.com/phpBB2/...iles/heart.gif (3 players)
BB checks, Hero checks, Button checks.

Turn: ($0.07) Jhttp://www.flopturnriver.com/phpBB2/...iles/heart.gif (3 players)
BB checks, Hero bets $0.05, Button calls $0.05, BB folds.

River: ($0.17) 5http://www.flopturnriver.com/phpBB2/...iles/heart.gif (2 players)
Hero bets $0.05, Button raises to $4.14,

Oops 4th nuts. Just saw 96h as a possibility.

I think that, while it's possible he may not have you beat, you'd be best off to wait for a better opportunity to take his stack.

Also, it's not a bad thing if he gets away with stealing tiny pots with pushes like this now and then. He will begin to think he can always get away with it and then suddenly you show up with a real monster and take it all.

fold pre, bet flop, fold river

Easy fold.

Also, like daven said, fold preflop.