I'd bet a bit smaller on the flop and larger on the turn. Something around 60-80% on both streets.

On the river I think I prefer a check and call. That gives villain the opportunity to bluff any of his missed draws and he still might shove worse Jx. The 7x on the river is a bad card for you but not bad enough to consider folding given the amount of money left behind.

If you choose to bet river I would just bet his entire stack. There's no reason to let him get off cheap the times he has a mediocre hand and let him put in the last 10bb only when he wants to.

As played, call the river raise. He doesn't have enough money to make you fold a hand like KJ since you're getting insane pot odds.