As I get started, just some preliminary observations:
In my bible, I can tell from what I've previously highlighted, that I was more interested in "fruit bearing" than I was "remaining." Whatever my state when I made those markings, looks like I was drawn more to output than input, effect than affect - to make some interpretive assumptions about my world at the time.
Is the passage more about fruit bearing or abiding? Was Jesus emphasizing one more than the other? One before the other? Like so much of the spiritual life, it is probably a false dichotomy; both/and versus either/or. But the question is worth asking.
I notice that the first two paragraphs begin and end speaking of fruit, in other words, have topic and summary sentences emphasizing fruit bearing. The third paragraph begins and ends with abiding. Though it has to be said that paragraphs in the English translation are translator decisions, not part of the ancient manuscripts. By the numbers (in my TNIV translation), there are 6 sentences that mention fruit bearing, 9 mentioning abiding, of which 2 refer to both in the same sentence. The actual word "fruit" or derivative of such occurs 9 times; abiding 11 times. What I really need to do is go to the Greek manuscript to see how these numbers differ, if at all.
On a purely devotional level, I wonder if Jesus knows that what the disciples desire is to "bear fruit" - that being associated with the visible signs of the kingdom of God/following Him - is what occupies their ambitions, their concerns; that they are intent on what great works will be credited to them, invested on what effects will stick with them as perceived by others. Or is that merely my concern? Whether that is a legitimate motivation or not, concern or not, Jesus makes no hint that it is not. I think the opposite is true - he validates the desire for fruit. But is the goal abiding or is it fruit-bearing? Or as I've said above, is that a false distinction? What seems to be clear is that there is no fruit bearing apart from remaining in him. One seems to be the necessity of the other. You can't put the cart before the horse no matter how much you might want to.