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 T, J.
1 fold, Hero calls $0.02, 4 folds, Button calls $0.02, 1 fold, BB checks.

Flop: ($0.07) 7, K, 8 (3 players)
BB checks, Hero checks, Button checks.

Turn: ($0.07) J (3 players)
BB checks, Hero bets $0.05, Button calls $0.05, BB folds.

River: ($0.17) 5 (2 players)
Hero bets $0.05, Button raises to $4.14,