Well, maybe she really likes you because you're such a nice person! A welcome change from the nasty men she's dated in the past.
And because you ARE such a nice person, of course you'd be willing to help out with the medical fees of her poor sick cousin. That's what nice men do. She's just waiting for the right moment to bring that up.
Of course, as Ashley Madison is a site for adulterers, most of the men on it are vulnerable to blackmail too. However, the amount of information you've been able to find out about her puts you in a good position. Make sure she can't find similar information about you.
If you are well-protected and ready for the almost-inevitable scam attempt, it could be interesting to see how far you get. Up to you, of course. But please keep us informed!