Standard Value bet or Check

[capone0]

Big Stack has around 1600 at the 2/4 PL 6 Max on PP on the big blind. I have around 300. Raise to pot-14 Bucks PF with AK. 3 Callers. Pot is 54 dollars. Flop is AK3, 1 diamond.

Standard I bet 40 on the flop. Turn is a another low diamond, I believe a 7. I bet 60. River is the 3rd diamond. He immediately checks. Pot is now 254. Do I check behind him or value bet. Big stack has been punishing people all day long but he usually big time value bets on the river when he hits. Lately, although at limit (5/10 6 max) I've been getting back doored like nothing else. Is checking behind him a weak play.