$1 NLHE MTT: value missed?

BTN: t1630 16.30 BBs
SB: t520 5.20 BBs
BB: t2795 27.95 BBs
UTG: t1325 13.25 BBs
UTG+1: t2260 22.60 BBs
Hero (MP): t2060 20.60 BBs
CO: t2910 29.10 BBs

Pre Flop: (t150) Hero is MP with A:heart: K:spade:
2 folds, Hero raises to t250, 3 folds, BB calls t150

Flop: (t550) T:heart: 4:spade: K:diamond: (2 players)
BB checks, Hero checks

Turn: (t550) 3:diamond: (2 players)
BB checks, Hero bets t255, BB raises to t510, Hero calls t255

River: (t1570) A:diamond: (2 players)
BB checks, Hero checks

Bet 200 on the flop.

River check is fine, we don't get much worse to call, don't want to get x/jammed on, and I'd assume our opponent is checking all of his value hands on the river expecting you to bet often.