I don't play anywhere close to this stackes, and I don't play live, but I remember several threads in HSNL, when OP took this line (my buddy also played a similar hand in 2000NL online) and OP had a set in all of them.

So I guess you should fold the turn.

I would also recommend raising less on flop: to 400, as there is only straigtht draw present and it will be easy to see if a straight draw completes on turn. Actually you don't need to worry about draws much, if OP has 97 or 53 he effectively has only 4 outs (otherwide straight will be too evident).
If you raise less on flop you'll have more chips for maneuvres on turn and river and your positional advantage will come into play.

She might not be bluffing, but maybe she thinks shes value betting but has the worst hand because shes a fool?

Also, the fact that her bet is only 1/3 pot doesnt really matter as much as it would if hero had 4000 left. Shes basically putting him all in even though shes only betting 1/3 pot.

It's sick, but you probably gotta fold that turn - I put her on A-8 or A-6 from how you described it. If she had 4-4, 6-6, 8-8, or the straight, than she probably would have re-raised the flop to protect. That under-bet on the turn was a sure-fire sign of a suck-out in PLHE, especially from goons who don't know what they are doing. She did just bet $650 into an $1800 pot, you know?

I also agree 100% with TableTager; live game players who are fishes LOVE the Ace like an unholy preist loves an alter-boy. They will play any A-x in any pot, in any situation. Dimitri Nobles and Tiffany Williamson are 2 well-known donk examples of this type of behavior.

And these people decide to play in a $10,000 buy-in tournament? If it wasn't for fish like that, poker wouldn't be a profitable living for so many damn people.