There's significant discussion regarding the ending of John and how disjointed it seems (specifically, chapter 20). This has led some to hypothesize that John's gospel has been edited a few times. These could be insertions from the Johannine community revising an original document.
Take it for what it's worth. I've also heard that could be a form of self-reference that is not necessarily self-aggrandizing. We tend to read something like "the disciple whom Jesus loved more than any others" but that may be an anachronistic reading of our own culture into the text. After all, didn't Jesus love all of his disciples?
Per John's request, here is a source that I could recall.
Craig L. Blomberg. Jesus and the Gospels 2nd Ed. (B&H: Nashville, 2009), 198.
There's a diagram that demonstrates a possible (thought not necessarily does the author indicate that it is firmly-established) path for production of the text which we currently have as The Gospel of John.
Hope that this helps.
2nd edit (to answer the question):
Sorry, I got so into the whole redaction thing that I failed to show how it could be a potential answer.
If it is the result of a series of redactions by a Johannine community, it could be their way of referring to John and does not actually represent the way he would self-identify in written fashion and they are the ones choosing to show us these things.
Having said that, even if this is the case, I believe in the infallibility of Scripture and that whether this was the work of several revisions, or of one person, the Holy Spirit intended for us to hear it. John may have been somewhat wealthy and notable (given the access that he has to the priest's courtyard) and, while Peter could be seen as the leader (CEO ?), John could have been the spiritually stabilizing force within the group. The person to whom even Peter looked for deeper knowledge, understanding, and spiritual support (if such things are not anachronistic).