She might also be proud. Peter is using his powers to help people, and Aunt May, being a kind - hearted person, would likely be proud of him for that. She could start to brag about him to her friends in a very discreet way, of course. And she would probably be more worried about him than ever, constantly thinking about all the risks he takes every time he goes out as Spider - Man.
Aunt May could also be a bit angry at first. Not because Peter is Spider - Man, but because he didn't tell her sooner. She might feel that she could have been more helpful or at least been there for him better if she had known. But eventually, she would come around and support Peter in his superhero endeavors.