I completely buy that Eve would be obsessed with Villanelle but the other way round? Nah mate.
I think Villanelle is obsessed and fascinated because Eve is her mirror-image/opposite – dowdily dressed, law-abiding (law-enforcing, in fact), hidebound by convention. It is very telling when she replaces Eve's clothes with beautiful and expensive new ones; I think she sees Eve as a project, to change into someone more glamorous, just as Eve has a project in Villanelle.
I think Villanelle is just so amused by the idea that someone is determined to stop her, she's decided to see if she can make that person love her instead.
And I agree with that too.
I don't fully agree with it being a male wank fantasy of a female serial killer. It makes sense that an assassin should be in good shape and young.
And yes, she wears expensive and often attractive clothes; there is almost a fetish element. But why should she NOT fetishise clothes? Take the James Bond films: the viewer is encouraged to notice and covet HIS clothes and watches, not to mention his weapons. I'd argue that in KE the clothes are actually used for more interesting and complex reasons (there's a good point in the article below about why someone of V's background might be into expensive clothes).
The voluminous pink dress is particularly interesting, I think. It ticks all the princess-fantasy boxes of being pink, frothy and girlish in shape, but it's a parody, an extreme version of a 'little girl party dress'. It says 'Yes, I'm wearing sugary frothy pink. And?' And it takes up a LOT of space, in an almost aggressive way, which is something women often don't feel we can do.
www.theguardian.com/fashion/2018/nov/02/how-fashion-both-decadent-and-drab-became-the-star-of-killing-eve