Éowyn has made walls around her heart.
Their construction began long ago, when she was young, following the deaths of her mother and father. Theoden broke them, but left the ruins where they lay, and as she watched her uncle and country succumb to Wormtongue's leechcraft they were rebuilt, taller and stronger than before. She thought Aragorn m ight break them; but he broke her heart instead, and Éowyn wonders if he was wrong in doing so, and ending her quest for power through marriage.
And now there is Merry, and she will not let him break them.
Éowyn is aware of how Merry looks at her at night when they stop to rest. Éowyn has far too often been looked upon with longing to be unable to recognize it. She has a feeling he hopes she will feel the same if he cares about her enough. The thought is enough to make Éowyn laugh, or cry. Because wouldn't that be something? To find she has feelings for Merry as she helps him find his way to war, and possibly to a death which he does not seek? She knows her goal – she will die, and she hopes her death will be honorable, but she has gone to end her life in glory. What does Merry want? To fight for his friends? And if he, too, dies, what then? To be one more promising life extinguished in the name of war is his fate. Éowyn has made a mistake in bringing him. She knows that, now.
But at the least, she may keep herself from caring too much about him. The walls around her heart have grown thick and broad, more than enough to keep a hobbit out, however kind and clever and free of guile his manner may be.
Éowyn must not care for Merry. They have chosen their paths, and they do not end happily.