We really don't see much of Edward in these opening chapters. The fact that he and Elinor are in love is just a throw-away line in Ch. 3:

"It was enough for her [Mrs. Dashwood] that he appeared to be amiable, that he loved her daughter, and that Elinor returned the partiality."

Elinor believes he returns her feelings, though she sees signs of "dejection" in him. Marianne derides his lack of demonstrative feeling in reading and art appreciation. He doesn't speak until Ch. 5 upon being told that the ladies will be moving to Devonshire:

"Devonshire! Are you, indeed, going there? So far from hence! And to what part of it?"

And that's it from Edward. Hardly lover-like, though there is some feeling in that "So far from hence!" line.

Why do you think JA showed so little of the interaction between Edward and Elinor? I think it because the novel she was trying to write was the conflict between "sense" and "sensibility" rather than conflict in love. But still... I could have done with a little less of Lady Middleton's "insipidy" and a little more of the relationship.