[Belegorn]

Éowyn never saw him, nor Faramir for that matter, as lesser men than they were. In Appendix A it is said:

"he seemed to men worthy of honour, as a king that is in exile, when he did not hide his true shape."

When they went to Edoras and she looked on Aragorn, "she now was suddenly aware of him: tall heir of kings, wise with many winters, greycloaked, hiding a power that yet she felt." [TTT, p. 141]

Although, at Rivendell Boromir doubted his ancestry, albeit, the kings were lost to the South Kingdom for many years.

Now at the Hornburg he appears to have revealed himself to the enemy as they were talking crap, "So great a power and royalty was revealed in Aragorn as he spoke to the Uruk-hai, as he stood there alone above the ruined gates before the host of his enemies, that many of the wild men paused and looked over their shoulders to the valley, and some looked up doubtfully at the sky." [171]

The Dúnedain who are like Aragorn are perceived by Éowyn to be pretty special, "for no mightier men had she seen than the Dúnedain and the fair sons of Elrond;" [RotK, p. 60] Earlier in the book they are compared to Aragorn, "stout and lordly men they are, and the Riders of Rohan look almost as boys beside them; for they are grim men of face, worn like weathered rocks for the most part, even as Aragorn himself;" [52-53]

The same thing happens when she meets a Dúnedan of the South Kingdom, Faramir, she saw him "and yet knew, for she was bred among men of war, that here was one whom no Rider of the Mark would outmatch in battle." [265] Recall how they were as kids to the Dúnedain of the North and likewise Faramir is above them.

In the end, Aragorn did not run from his purpose. He had been fighting against Sauron at least since his 20s, helping out other kingdoms under various guises. Arwen had even wrought a banner for him as the king before he would become so.