is this a bet or check behind on the turn

[LAgambol]

10/20/40 NL

Villain got stacked earlier by me, he reloaded and has been winning since. He's been gambling it up and was definitely a loose player. He was calling down light in the session. Hero has been playing LAG.
Villain has 8K, Hero covers

1 limper, Hero in LP Jc10c calls, BB calls, villain in straddle makes it 240, limper calls, hero calls, fold

Flop:
Jh10d5s

villain bets 500, limper folds, hero makes it 1600, villain calls

Turn:
Kd
villain checks, hero...

thoughts on all streets appreciated