Poker: Tough Spot with pocket Aces

Probably a standard river fold, not sure about turn. There's probably a case for a tight turn fold (?) although not sure. Thoughts on all streets appreciated.

handed 10/20 live game. LP ($5K) limps, BTN ($5K) raises to $60, folds to me in BB ($2K). I raise to $200, both call. BTN is a tough reg capable of making moves. He should view me as a good/tight player. I have Ac

Flop JcTc6s. I bet $400, LP folds, BTN thinks for ten secs, asks to spread the pot, thinks for another ten seconds and calls. Turn 6c. I check, he bets $400. I call (?). River 9s. I check, he bets $700, I fold.

I've played a lot with BTN (though not necessarily hands against him) and he should know that my range here is QQ+. I feel like if he floated the flop to try and rep the flush, that he would bet bigger on the turn. He knows I can fold QQ-AA here. Maybe he flats TT/JJ on the flop IP. Anyway, with his sizing, I felt like he was trying to milk me. When he fires the turn in this spot, he's pretty much always betting the river too so maybe.. I could have found a turn fold? Thoughts?