Family

Eowyn is mentioned far before she actually enters the text. Galadriel sees her as a wife for Aragorn due to her foresight, and makes this quite clear in a message to him;

Elfstone, Elfstone, bearer of my green stone,
In the south under snow a green stone thou shalt see.
Look well, Elfstone! In the shadow of the dark throne
Then the hour is at hand that long hath awaited thee.

Eowyn is "in the shadow of the dark throne". Obviously, this version of Galadriel's message never made it, since Tolkien resolved to rewrite it when he cut out of the love story of Eowyn and Aragorn (see below).

Eowyn entered as little more than a scribbled note on a page. In the first texts of 'The Riders of Rohan', as a note to himself, he wrote "Eowyn Elfsheen Daughter of Eomund?" On the back of this page, there is also the note "Eowyn Elfsheen daughter of Theoden".

So Eowyn, from the start, was a lady of high status. However, she was now the daughter of Theoden, and therefore of higher status than what she became, the daughter of his siter. The name 'Elfsheen' indicates that she was beautiful, that she had a different beauty than her future counterpart; that she had the perfect beauty of the Eldar, and was more the classic lady on the surface such as Arwen.

The second instance of Eowyn in the writing was in an outline. 'Eowyn sister of Eomer waits on the guests. Description of her, and of her love for Aragorn.'

Already her love for Aragorn is mentioned, before she enters the written prose; at this point, she was not to be the warrior we knew in the final drafts, but a wife for Aragorn.

When Eowyn is first mentioned in the next, it's as she is helping Theoden down a hall: he says to them, "Go Idis, and you too Eowyn sister-daughter!" So Eowyn is no longer Theoden's daughter, but the character of Theoden's daughter has not been scrapped yet; she is now Idis. However, Eowyn overshadows her, and gets a mention after she and Idis have left: "very fair and slender she seemed. Her face was filled with gentle pity, and her eyes shone with unshed tears. So Aragorn saw her for the first time in the light of day, and after she was gone he stood still, looking at the dark doors and taking little heed of other things."

And here enters the love story of Aragorn and Eowyn, which obviously never made it to the final text. It seems that it was cut out somewhat early, so there are few romantic moments between them, and a final wedding between them was never written. However, other than the first meeting, there are some moments; at the meal before the departure, 'Aragorn was silent, but his eyes followed Eowyn', and when she brought wine to guests, 'Long she looked apon Aragorn, and long she looked upon her' and also 'As she stood before Aragorn she paused suddenly and looked upon him, as if only now had she seen him clearly. He looked down upon her fair face, and their eyes met. For a moment they stood thus, and their hands met as she took the cup from her. "Hail Aragorn son of Arathorn!" she said.' Also, Aragorn says to her before his departure, 'If I live, I will come, Lady Eowyn, and then maybe we will ride together.' After this, Eowyn 'smiled and bent her head gravely'. And, in an outline for matters to be touched on, in it is listed 'Aragorn marries Eowyn sister of Eomer (who becomes Lord of Rohan) and becomes King of Gondor'.

I think it is made evident from this passages that this woman, Eowyn Elfsheen, is a different one than the Eowyn we know. A bit like the difference between Book Arwen and Movie Arwen; Eowyn Elfsheen is more willing play the classic lady, and more content with her role in society; she's more willing to stay off the battlefield, and more secure in her love for Aragorn. The only issue for her is the fact that the timing itself is terrible; Aragorn could be riding out to his death, and there's nothing she can do about it.

Eowyn Elfsheen is far more like Arwen Undomiel, in my opinion; though Arwen has her many insecurities and doubts about her relationship with Aragorn, they are (mostly) settled by the time she and Aragorn marry. She is willing to stand aside and take no active part in the war of the ring, while the Eowyn we know is not. Despite Tolkien having Aragorn marry Eowyn at first, he still marries a character much like Arwen, the woman he would eventually marry.

The relationship between Aragorn and Eowyn, as I said before, did not last long. Tolkien had decided to cut it, due to Aragorn being 'too old and lordly and grim' for a love story at this point in his life, and especially for a lover as young and innocent as Eowyn Elfsheen. After this break is when Eowyn emerges as the character we know, 'a stern amazon woman', as Tolkien describes her, and twin sister of Eomund. Now she is an older figure (although I doubt this lasted long at all), the sister of someone who was once her father; however, Aragorn still loves her (although there isn't any mention of she loving him in the outline, we can still assume it is so that she still loved him) and Tolkien wrote to himself the idea that Aragorn did indeed love Eowyn and never married after her death. Now their love is a more tragic tale, like that of Andreth and Aegnor. The original plan was that she would die in this incarnation, to save or avenage Theoden; and it stayed this way for a while, to the point where he wrote several versions of her death. (transcripts coming soon). However, with the emergance of Faramir, this changed, and well, we all know what happened after that. :D