2/5 live: AK versus an odd line

[ICallHimGamblor]

Hero sees AKo under the gun and raises to 30. Called by BB.

Flop ($60): K 8 4 rainbow
BB checks. Hero bets $60, BB calls.

Turn ($180)(K84): J bringing two diamonds.
BB checks. Hero bets $130, BB calls. Hero is now very suspicious.

River ($440)(K84J): T resulting in no flush.
BB checks. Hero???

Here is my problem: I have no read on him and I have no idea what this guy could have.
Busted flush draw? There was no draw on the flop and he called.
Two pair or set? Why didn't he bet on the river?
Some weird gutshot straight? If he got there, again, why didn't he bet the river?
I figured him for a worse K, but if so, he probably isn't calling the river.

So the question is: am I betting for value here, or is it spewy to bet here when I have no idea where I am?

Comments on all streets welcomed. Thanks.

[DaCooler]

i gladly check the river here and get to showdown without a massive read as this guy being a huge donkey CS, you got two streets of value and your not that strong anymore, just show it down, the only hand you really beat here is KQ