Playing aces passively

[soah]

Last week I was playing in a game with $1/$1 blinds. The game is loose/passive with many hands going unraised before the flop. Sometimes people will randomly bet $12 all-in with QT and get called by A5 and K8s. Sometimes big raises do mean really big hands though. My opponent in this hand has been overbetting the pot regularly when she makes 2 pair, a set, etc. (And someone always pays her off, of course.) Some of the hands she plays are pretty trashy. Earlier I raised with AK and she busted me after making 2 pair on the turn with K5 after I was fairly committed to the pot.

I am reconstructing the hand in question from memory so details will be somewhat sketchy. I think I had around $70; she had quite a bit more. She was in early position, I was somewhere around the CO.

Pre-flop: She opens for a raise to $7. It's folded to me; I have AA. I haven't seen this from her yet, so I am assuming she has a premium hand, but I'm not yet ruling out hands like AT or 99. I decide just to call in hopes that someone else might tag along, and so that she'll bet into me on the flop.

Flop: The flop is 998 rainbow. She does indeed bet into me; about $10. This is definately not the flop I was hoping for, but I think it's pretty unlikely she holds a 9. If she raised with 88 then I'm screwed. Normally she overbets the pot if she has trips, so I put her on something else. I consider raising, but I'm afraid that doing so may cause her to fold hands that have very few outs (basically any hand other than JT, which I doubt she'd raise to $7 with). I definately don't want to scare her off if she holds something like AK which is nearly drawing dead. If I'm wrong and she does have me beaten, then of course I don't want to raise. I'd also like her to keep betting into me with a weaker hand.

Turn/River: The turn is a brick. She bets into me again, around $20. I call for the same reason as I did on the flop. The river is another brick, and she bets about $15. Calling here leaves me with some chips. The fact that she bet less on the river than the turn makes me even more certain that my aces are still good. I consider pushing, but decide against it. She's not a maniac, and she knows I'm not a calling station. Raising with unimproved aces at the river simply doesn't seem like good play. I call; she shows JJ, I win a pretty big pot.

I've had nagging doubts about this hand ever since it happened. By playing passively, I was able to get her to invest quite a bit of money trying to make her overpair hold up. I don't know if she respects my play enough (and is good enough) to fold at any point in this hand had I raised. Normally I don't play aces like this, but normally the pot isn't raised 7BB in front of me... did I play the hand badly or was it ok to simply let her continue firing every round?