weak ace blind defense

[geormiet]

Online 20/40 6 handed
villian is a decent lag regular. My notes say "missed riv value" but i think overall he's just normal not too bluffy and not too weak.

Villian raises co, i call in BB with Ac5d.

Flop is 944 with 2 diamonds. I check, he bets, I call. Turn is an offsuit Ace. I check, he bets *pretty* quickly, I wait for about 1-2 seconds and call.

River is Jd. I check again because donking feels stupid here.

Anyone suggest alternate lines?

If you are villian how would you play the turn/riv if you had either KK or JT?