I reckon i'm ahead vs idiot in question at least 85% of the time. He gets lucky and draws to Aces up sometimes but he's calling flop, turn, river bets with middle pair and any Ax. So why not bet this river?

PokerStars Pot-Limit Hold'em, $0.25 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG+1 ($22.50)
MP1 ($38.65)
Hero (MP2) ($29.15)
MP3 ($29.15)
CO ($25)
Button ($35.30)
SB ($18.25)
BB ($25.35)
UTG ($25)

Preflop: Hero is MP2 with 10, A
1 fold, UTG+1 calls $0.25, 1 fold, Hero bets $1.10, 2 folds, Button calls $1.10, 3 folds

Flop: ($2.80) 4, A, K (2 players)
Hero bets $1.50, Button calls $1.50

Turn: ($5.80) 2 (2 players)
Hero bets $4, Button calls $4

River: ($13.80) J (2 players)
Hero checks , Button checks

Total pot: $13.80 | Rake: $0.65