Re: a pair of 40/80 bb hands
hand 1: fold PF, fold the flop, fold the turn. Even if she's not a rock, A7o is likely way behind her PF raising range from EP, and you've got terrible RIO. You completely missed the flop and I think you are going to have a hard time getting her to lay down any sort of hand at all. Players like this, in my experience, tend to play tightish PF, but when they get involved in a hand they get very stubborn (especially heads-up).
hand 2: I'd probably just call the flop, call the turn, and fold the river u/i (obviously raise the turn or river if you catch your straight or back-door flush). There's no point in getting fancy in a nearly dry side pot, since you'll never beat the all-guy with the 2nd nut low.
In general, when you move up a limit I think it's best to play pretty straightforward at first and consciously avoid fancy plays. There was a big thread about moving up a while back, and a lot of people said the same thing.
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