I’m of this guilty, too.
There’s this warped conversation filler that people — busy people — use to signal their attention to another speaker and urge that conversation along. I say it’s warped, because listeners are not supposed to supply conversation fillers; normally, the speaker gets to “like,” “um,” and “I mean,” and “ahhhh” her listener to death. A speaker uses a filler to give herself time to think and still hold the floor while she’s formulating the words for the rest of a thought.
However, there’s a new conversation filler in town: “Right, right, right, right…” Sometimes when I’m speaking — and quite clearly and steadily — my interlocutor, who’s supposed to be listening, will interject or, really, voice over my sentence with the rapidly repeated word “right.”
It goes like this:
Jane: I’m wondering if my tendency to wear a shoulder bag rather than a back pack —
Chiropractor: Right, right, right, right…
Jane: — is in part the cause of my impaired neck.
Many people do this, start talking over another person’s sentence. It’s possible that “Right, right, right” is supposed to convey that the “listener” is in sympatico with the speaker.
However, this is how it sounds to me.
Jane: I’m wondering if my tendency to wear a shoulder bag rather than a back pack —
Chiropractor: Hurry, hurry. I know this already! It’s my turn to talk.
Jane: — is in part the cause of my impaired neck.
Dear listeners, it’s okay to make eye contact occasionally, say “hmmm,” nod, and even wrinkle your brow at the person who is talking. But the right, right, right, is — forgive me, I can’t help myself — wrong, wrong, wrong.
I’ve done it, too, and now I’ll be very careful and stop.
leaf stitch word 
What a great observation! I’ve noticed this, too. I know someone who does it so…. aggressively?… that it seems like she isn’t listening at all. She *is*, but you would only know that if you know her. It’s pretty irritating.
I often have to listen to myself do this annoying crap when I listen to fieldwork tapes over and over again while transcribing. This past summer, I took an audio workshop where the instructor urged us to avoid this kind of thing as much as possible, since it really screws up the usability of the recording (you can’t get a “clean” version of what the pther person’s saying).
He quoted some famous female radio personality (and I’m afraid I don’t remember who it was, specifically) who advised people, “Don’t interview like a woman” — i.e., knock off the annoying verbal feedback that (allegedly) indicates we’re listening and following and understanding.
It was a revelation to me! I find that I still have a hard time breaking the habit. As you wisely note, though, Jane, it may not *be* as reassuring to the speaker as we think it is, anyway. Another good reason to give it up.