Isn’t it ironic that Éowyn fell in love hopelessly with a man whose (Elvish) name (Estel) means hope? (Not that she would have known that name… ) It touches me that the love story most vividly described in LotR should be one of unfulfilled love.
Some call it infatuation or a crush; no matter – it is a form of love Éowyn felt, a serious emotion as she experienced it. Who can blame her? Any decent man would have looked good next to Gríma, the one who wanted her and plagued her existence daily. And let’s face it, Aragorn was an unusual specimen – they don’t make them like that nowadays!

(If they did, I’d be first in line and fighting to stay there!

And yes, I am talking about the book character, not a movie actor.) Who wouldn’t fall for him?
What I wonder is, what good came of Éowyn’s unrequited love? Would she have acted differently had she been happy and content, whether in or out of love? Was it the desperation of hopeless love that gave her the recklessness to go to war as a shieldmaiden and perform her great deed? Does love lift the one loving above her/himself even when s/he is not loved in return? Is there any truth to Tennyson’s statement that “It is better to have loved and lost, than never to have loved at all.”?