Given the size of the blinds
A check on the flop shows weakness, and she'd be likely to bet first instead, forcing you to call or fold A/K, which you can't really do at this point. Betting first at gives you a chance to win it right there.
With blinds that high, and her not raising, you pretty much have to go for it from there on in. An A/K on the river, and you'd have been looking good!
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