5/10 hand I found interesting

[Bartholow]

I have KKJT with 3 hearts, 2nd to act. UTG folds, I raise to 30, folds to SB who calls, BB folds. Don't have a ton of hands with SB but she's seen the flop 80% of the time and has never raised preflop. No real read on postflop tendencies, seems kinda loose? She has 500ish chips, I have her well covered. My image is probably kinda laggy.

Flop is Ad 2d Ks, she checks, I pot, she calls. Turn is Ah. Pot is about 210, she's got 400ish left. What's the plan?

My thinking was she's probably got some sort of draw here, just because there are some decent draws but less ways to have too "made" hands given the cards that are out and if she had flopped something she really liked wouldn't she have to play back at me on flop, as I could have any of those draws and she wouldn't want to have turn come with no information. So anyway, I think about it and figure hard to get called by many hands I beat, maybe I can get a bluff or get her to hit a no-good hand on the river, so I check behind. I guess I was thinking free card is no problem here, especially since she's not deep enough to get away from an ace that hasn't filled. Does that logic make sense or should I fire here hoping a draw will pay to draw dead?