This is an interesting question, and the examples used to highlight it change at different points in the story. When the story first begins, it is more obvious that Gene's identity is more co-dependent on Finny than the other way around. They are best friends, and they love sharing that identity with the world:

"It's you, pal," Finny said to me at last, "just you and me." He and I started back across the fields, preceding the others like two seigneurs.

We were the best of friends at that moment.

While being best friends, I believe that Gene is more dependent on Finny because Finny is such a charismatic, care-free, athletic, fun, and confident kid that I believe that he would be just as happy with a different best bud. Gene on the other hand gains a bit of social status by being Finny's best friend. It's not the other way around. Finny remains who he is for a great deal of the story; however, he does become more dependent on Gene. In an understandable and sad way, Finny begins to vicariously live through Gene. Finny puts his athletic hopes and dreams on Gene, and Gene obliges most of it. The two become more and more bound to each other, and by the end of the book, Gene recognizes this fact, as he says,

My aid alone had never seemed to him in the category of help. The reason for this occurred to me as the procession moved slowly across the brilliant foyer to the doors; Phineas had thought of me as an extension of himself.

By the time Finny dies, the two boys share such an identity that Gene doesn't even cry at Finny's death or funeral. He doesn't cry because it doesn't make sense to cry at his own funeral:

I did not cry then or ever about Finny. I did not cry even when I stood watching him being lowered into his family's strait-laced burial ground outside of Boston. I could not escape a feeling that this was my own funeral, and you do not cry in that case.

John Knowles' novel A Separate Peace addresses the ideas of identity and codependency through the relationship of Gene and Finny.  Gene is co-dependent on Finny, the easy going, well-liked student at Devon, and as the novel progresses, Gene realizes that he has grown weary of his sidekick status.  Gene wants more for himself and struggles to invent himself as a young man and a student.  Naturally gifted academically, Gene also wants Finny's easy athleticism.  Gene envies Finny's natural charisma, his ability to "combine a calm ignorance of the rules with a winning urge to be good" (16).  Ultimately, Gene's jealousy of Finny causes him to lash out and cause his friend's accident; even then, it is Finny and his natural goodness that help Gene define himself.  In this sense, Gene is co-dependent upon Finny, because Gene fails to see his admirable qualities in himself; it is his own struggle for identity that draws him to Finny.  Finny sees the best in Gene, even when Gene cannot, and it is Finny's insistent forgiveness that day in the infirmary that finally opens Gene's eyes to his own potential for good.

If there was ever a co-dependent relationship, it had to be Gene and Finny--at least, from Gene's side.  Gene's friendship with Finny is tainted by envy; while Gene does well in school, Finny is the more gifted athlete, and as in athletics, life excluding academics, seems to come very naturally to Finny.  Finny is carefree, happy-go-lucky, able to talk his way out of most any sort of trouble--and what Gene absolutely cannot tolerate is when he figures out that Finny does not feel a reciprocal jealousy of his (Gene's) hard work and academic success.  So, like in any co-dependent relationship, Gene's "friendship" with Finny is not really a friendship as much as an unhealthy emotional attachment to what Finny represents.  As much as Gene feels resentment and irritation toward Finny, the idea of not being part of Finny's carefree, jovial, amiable life is more intolerant to him.  When Gene jiggles the tree and causes Finny's accident, the need to be part of the fun has been trumped by the malevolent feelings Gene carries toward his "friend".