SH NL2 33 from MP

Notes on Villian:

Since villian sat down he has limped or limped called almost every hand
77/3 over 196 hands and limp% of 87

My question is it correct to go broke on the river?

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.01/$0.02 No-Limit Hold'em (6 handed)

Known players:
[tg]BU$3.02:///////;SB$2.00:///////;BB$1.37:///////;MP2$2.99:///////;MP3 (Hero)$4.72:///////;CO$2.10:///////;[/tg]

Preflop: Hero is MP3 with 3:s, 3:d.
MP2 folds, Hero raises to $0.06, CO calls $0.06, BU calls $0.06, 2 folds, BB folds.

Flop: ($0.21) 2:s, A:c, 3:c (3 players)
Hero bets $0.10, CO folds, BU calls $0.10.

Turn: ($0.41) T:d (2 players)
Hero bets $0.30, BU calls $0.30.

River: ($1.01) T:s (2 players)
Hero bets $0.80, BU raises to $1.60, Hero raises to $4.26, BU calls $0.96(All-In).

Final Pot: $7.83.

Results follow:

Hero shows a full-house, threes full of tens(3s 3d).
BU shows a full-house, tens full of aces(Ah Th).

BU wins with a full-house, tens full of aces(Ah Th).