Hit me with it!

[PKKFW]

MP is 74/24 over 68 hands has called 100% of three bets and post flop was pretty much a calling station as well.
button is 12/9 over 209 hands. Seems pretty solid.

My main question is should I be betting the river or checking behind? I know I should have bet the flop and really have no idea why I didn't.

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) - PokerStars Converter Tool from FlopTurnRiver.com

SB ($4.41)
BB ($12.26)
UTG ($3.81)
MP ($12.17)
Hero (CO) ($15.11)
Button ($10.10)

Preflop: Hero is CO with 10, 10
1 fold, MP bets $0.40, Hero calls $0.40, Button calls $0.40, 2 folds

MP would call a 3 bet no matter what so with 10's and a few to act behind as well I didn't want to raise here. My plan was to see the flop and see how we go.
At this stage I'm putting MP on any two cards.
I'm putting button on AK, AQs is possible but not likely, any pocket pair.

Flop: ($1.35) J, 8, 10 (3 players)
MP checks, Hero checks, Button checks

As previously mentioned I have no excuse as to why I didn't bet this flop. It's a draw heavy flop and I should not have been mucking around giving free cards. Total brain fart. MP would almost 100% have called as well so it would have built the pot some too. Huge mistake.

With both players checking I'm putting button on AK, AQs or pocket pair that missed trips.
Because I checked I have no way of narrowing down MP's range and that just compounds my mistake obviously.

Turn: ($1.35) A (3 players)
MP bets $0.40, Hero raises to $1.60, 1 fold, MP calls $1.20

Ok, now I'm pretty sure he has Ax. I raise expecting a call.

River: ($4.55) 9 (2 players)(2 players)
MP checks,

Bet or check?