She's 'fond of' asking silly questions. [=she asks a lot of silly questions]
She has 'fond' [='cherished, warm'] memories of their time together.
She is still 'fond of' him. [=she still likes/loves him]
(..) I would love to be there if I could get a box. You'll find me there with Princess Myagkaya. Will you come, Vronsky? -Well... -I see why Alexei is so fond of you. You know you can't go to the theater. -Annushka! -For heaven's sake. A bath! I'll come in and choose a dress. Anna, I implore you. (..)2012 Anna Karenina
(..) The last one was to meet a missionary. The one before that was for a lecture on the union of the Greek and Roman Churches. Oh, I'm sorry. I know you're fond of her. Come on, or we'll be late. Here's the thing, Vronsky. A posting's come up, and there's a promotion in it for you. Thank you, sir. (..)2012 Anna Karenina