Super thin value shove in the Million

[Eagles]

Not much of a read on villain. If he's paying any attention He views me as really crazy because I've been playing like a monkey. I was prob playing like 45/30 or something in level 1 and lost a lot of my stack when i 3bet pf with 58s the guy donked and I shoved for pot with 8 high no draw and got insta called by A Q high no draw. From that point I just won a bunch of races etc. And have a solid stack. Anyways on to the hand.

Blinds are 200/400

Effective stacks are 10k

Villain limps UTG folded to Hero on the button who makes it 1600 with AJo Villain calls.

Flop is

Tc 8s Kd

Villain checks
Hero checks back.

Turn 6c

Villain checks
Hero bets 2500
Villain calls.

River Jd
Villain checks
Hero?

Pot is like 9k and Hero has 6k behind. Who bets who checks? If I bet how much?
If the river is the jack of clubs does that change anything?