Eowyn is certainly attracted to Aragorn, but Faramir sums it up in the RotK when he says she looks up to him like a young soldier to a great captain. She loved him even though she knew it was impossible that they could be married, as Aragorn already was enaged with Arwen. It is still easy to love somebody though, even when you know you know they may never love you back (as is often with my case).
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