villian was 16/15/3/8 over 200 hands

Not sure what you're hoping to achieve with the 4b pre, doubt anything better folds or anything worse calls, just close the action and play poker

What is villain's three bet %?

have to agree with sixfour... pre flop call and close the action.
The turn is an Easy Fold

I think the 4bet is fine, but calling is also viable. When you 4-bet, you're hoping to win the pot immediately, but it's also fine if villain(s) will flat with worse. Just remember that this will be the bottom of your 4-bet range (apart from AK and any random 4-bet bluffs), so you can/should check-fold JJ on bad flops, like Axx. As sick as it sounds, when you've put so much money in the pot pre, you should fold to a 5-bet jam, as that will be QQ+/AKs or even just kings+.

You can check or bet this flop, but getting stacks in before bad turns is pretty crucial. You're gonna run into QQ or slowplayed aces sometimes though. (You can basically ignore BB. He's usually capped at TT or has something random like AQo or KTs and he has no clue how to play pre-flop. i.e. He should never press the CALL button twice pre-flop).
FWIW, I don't think villain should call with AKo on the flop. If you have 18 combos of JJ+ in your range, he only has 22% equity (he has less if you only jam QQ+), but the pot odds require 25% (plus about 5% more for rake), and he's not even closing the action, so you can consider this a bad beat.