O'Neill has Eben look up to the sky in order to communicate an important aspect of his character.
As the play opens, O'Neill uses stage directions to communicate important elements about Eben. After the first time Eben speaks in Scene I, O'Neill includes these directions:
His [Eben's] defiant, dark eyes remind one of a wild animal's in captivity. Each day is a cage in which he finds himself trapped but inwardly unsubdued. There is a fierce repressed vitality about him.
Eben's habit of looking up to the sky is a way to communicate his imprisoned nature. In looking to the sky, Eben looks to being free. O'Neill is able to remind the audience of how Eben sees life as "a cage." His ability to look up to the sky represents a search to find a way out of the trapped existence he leads. In looking at the sky, Eben finds a temporary outlet for his "repressed vitality." Eben's looking at the sky communicates this to the audience throughout the drama.