Better to check call river, or shove?

[DJJunkPauds]

Villain is 25/11 over 100. Notes on him read:

* Cold called with KQo
* Checked called 3 streets with TPGK
* Cold called with SCs/Gappers
* Bet his draw.

PokerStars No-Limit Hold'em, $0.05 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

MP ($1.99)
CO ($5.11)
Button ($6.08)
Hero (SB) ($5.35)
BB ($7.09)
UTG ($5.60)

Preflop: Hero is SB with Ad, Qc
1 fold, MP calls $0.05, CO calls $0.05, 1 fold, Hero bets $0.30, BB calls $0.25, 1 fold, CO calls $0.25

Flop: ($0.95) Qs, 8h, 9c(3 players)[/color]
Hero bets $0.70, BB calls $0.70, 1 fold

Turn: ($2.35) 2s (2 players)
Hero bets $1.60, BB calls $1.60

River: ($5.55) 3s (2 players)
Hero bets $2.75 (All-In), BB calls $2.75

Total pot: $11.05 | Rake: $0.50


I think I would have been better off check calling the river.

Please explain your thinking.

(Converter code is messed up in preview, hopefully it'll work on submission)