It seems that we language bloggers haven't been holding our end up on this one. Back in 2007, Dave's Midlife Blog looked in vain on Language Log and Language Hat for an analysis of the phrase that Jeremy uses in the last panel:
When the phrase “I know” is used in English […], it signifies assent and acceptance of the point of view of a conversational partner. It’s a fairly confident assertion of acknowledgement, of agreement.
On the other hand, the questioning “right?” stuck onto the end of a sentence is a request of affirmation of an assertion and a simultaneous invitation to disagreement. Right? Don’t you think so? Do you agree with me?
So when a young speaker (and I’ve only heard this phrase used by speakers under the age of 25) combines the two, it seems to be a simultaneous assertion of confidence and an instant pulling back of that confidence so as not to seem too pushy. It seems to ask for a continuation of the conversation. If the interlocutors continue the conversation, it may branch into areas of disagreement, but so far they are of the same mind.
I tried to find a discussion of this on Language Log without success; likewise with Language Hat.
All he could find was some peeving on Le Mot Juste:
And what does it even mean? That you have an opinion, but you need my permission to validate it? Don't ask me if you know immediately after you tell me you know. Either you know or you don't know. The next time you say, "I know, right," expect me to say, "no, you're wrong. You obviously don't know, so don't waste my time trying to convince me you do."
This analysis didn't satisfy Dave — as he sensibly observed,
I don’t think that would actually happen in conversation, because I don’t think the phrase would be uttered if there weren’t already some basic agreement present …
The New Thing is certainly not the idea of agreeing with someone's opinion and then appearing to ask them to confirm it again, as further validation rather than as an expression of doubt. Ways of doing exactly that have been around for a long time, without (as far as I know) anyone noticing or complaining. Thus in William Archer's 1890 translation of Henrik Ibsen's A Doll's House:
Nora. Ony think! my husband has been made Manager of the Joint Stock Bank.
Mrs. Linden. Your husband! Oh, how fortunate!
Nora. Yes, isn't it? A lawyer's position is so uncertain, you see, especially when he won't touch any business that's the least bit . . . shady, as of course Torvald won't; and in that I quite agree with him.
This pattern is a common one — you can find it in William Dean Howells 1907 play A Previous Engagement:
Mrs. Winton: "How delightful! Why, it's quite like something improper!
Mr. Camp: "Yes, isn't it?"
Or in Agatha Christie's 1959 crime novel The Cat Among the Pigeons:
'That's very vague, Miss Rich.'
'Yes, isn't it?'
Now, the same sort of peeves ought to apply to these cases as well. When someone has just offered an opinion, and you've agreed with it, how can asking them to confirm the evaluation reinforce your agreement rather than subtracting from it?
We can see the answer in passages where the author tells us more about the thoughts and feelings of the participants in the exchange. Thus Alexandra Potter, The Two Lives of Miss Charlotte Merryweather:
Her jaw drops. "Oh my gosh that's just . . ." She trails off, words failing her momentarily, before coming alive again. "Splendid!" she gushes finally. "Simply splendid!" She beams at me, almost trembling with excitement.
Watching her reaction it suddenly throws my own into contrast. She's absolutely right. It is splendid. Though I'd probably choose to describe it as fantastic, I think, bemused by Beatrice's choice of adjective.
"I know, isn't it?" I enthuse, mirroring her excitement.
"Absolutely. It's amazing," she whoops, …
Charlotte and Beatrice are "mirroring" feelings back and forth. In this context, the question "isn't it?" is an invitation to continue the process, and it therefore intensifies the shared evaluation rather than attenuating it. And you can see the same process in stereotyped "right?" examples like this one:
So why do people react when "right?" is used for this purpose instead of "isn't it?" Well, the obvious answer is that they're not used to it. This usage, or at least its frequency, may be something new. As usual, we should check for the "recency illusion", but there's no question that many people perceive this as a new (over-)usage. Thus in a November 2010 forum discussion in response to the prompt "describe your classmates" one young person characterized four of them as "'Gee like OMG totally right?' kind [of] girls".
In addition, this mirroring or intensifying "right?" can be used in a much wider range of circumstances than the mirroring or intensifying "isn't it?". Thus in Greg David, "Tek finds love", TVGuide 8/18/2009:
TVGuide.ca: I’m sorry you got eliminated so soon.
Tek Moore: Yeah, it’s a shame, but it’s all right.
TVG: I like that you shot the devil horns as you walked down the hallway though; was there a significance to doing that?
TM: I know, really, right? I was relieved to be done. I know that I can cook, but I was having some serious malfunctions cooking in Hell’s Kitchen… it was so stressful and so tough… it was kind of like, ‘OK, I can breathe easy now’ once I knew I was finished. I left with a positive attitude.
We can't idiomatically substitute "I know, really, isn't it?" in this case, because the evaluation being mirrored ("I like that you shot the devil horns") doesn't make an antecedent available for the it of "isn't it?".
So OK, Dave, it's four years late, but there you go.
Update — someone felt strongly enough about this to create and post an elaborate youtube peeve "Stop Saying 'I know, right?'" and an associated Facebook group. Neither one seems to have gotten a lot of traction. In a more sympathetic vein, here are some acted examples from this video: