This has become kind of a thing in recent years in comedy movies and TV - someone asks a question, and someone else answers with mock solemnity, almost awe, “Yes. Yes, it is” or “No. No, it isn’t.” Who first did that?
For future thread searches: yesyesitis yesyesitis yesyesitis
First thing I thought of was The Simpsons episode “Homer’s Barbershop Quartet.”
A reporter asks Principal Skinner if his reputation as ‘The Funny One’ is deserved, and he responds with a very monotone,
“Yes. Yes it is.”
I haven’t noticed what you’ve mentioned, but it’s very close to a device that I’ve seen used many times, also in a solemn way. What I’ve seen is more like “Yes, I know, Paul. I know.”
No idea how far back that goes, though. Happy hunting. 
That was Airplane II, and that’s not quite solemn enough.
Wellington came close to it at Waterloo:*
Lord Uxbridge: Good God, I’ve lost my leg!
Wellington: Yes, I believe you have.
*Though it could have been in use even before that, I suppose…
IMDB search for quotes indicates a first use in an episode of Friends, 1995, but that’s just the first one that somebody put into IMDB. It could easily have been in use before that. However, this does sound like a very Ross kind of comment.
Ghostbusters 1984
Dr Ray Stantz: Everything was fine with our system until the power grid was shut off by dickless here.
Walter Peck: They caused an explosion!
Mayor: Is this true?
Dr. Peter Venkman: Yes it’s true.
[pause]
Dr. Peter Venkman: This man has no dick.
Very similar to your premise.
Yeah, I was going to say that I associate the line with Bill Murray’s deadpan style.
Edit: the scene in question.
No, I remember Murray in Ghostbusters very well, but as I mentioned in the OP, it’s the repetition of the word “Yes” or “No” that sets it apart.
Kent Brockman: When cat burglaries start, can mass murders be far behind? This reporter isn’t saying that the burglar is an inhuman monster like the Wolfman, but he very well could be. So, professor: would you say it’s time for everyone to panic?
Professor: Yes I would, Kent.
…later…
Kent: Hordes of panicky people seem to be evacuating the town for some unknown reason. Professor, without knowing precisely what the danger is, would you say it’s time for our viewers to crack each other’s heads open and feast on the goo inside?
Professor: Mmm, yes I would, Kent.
The first time I read it was in Jhonen Vasquez’ comic Squee! back in 1997, and possibly Johnny, the Homicidal Maniac. Jhonen Vasquez is, of course, the genius behind Invader Zim, another character who deadpanned “yes, yes it is” to awesome and hilarious perfection.
An episode of Sanford and Son, mid-1970s.
Fred’s doctor orders some tests. They are routine, but they do require him to stay in the hospital overnight. Fred finds himself sharing a room with another elderly man, who seems to be in some pain. The nurses are fairly lackadaisical toward Fred, but whenever they look at the other man’s chart, they fuss and fawn over him. Fred decides that he wants some of that attention, so he switches the charts.
A doctor and several nurses enter the room, dressed for surgery. They take a quick glance at the chart, and start wheeling Fred’s bed out of the room. Lamont enters the room. Upon learning that Fred is being taken to surgery, Lamont protests that there must be some mistake.
The doctor looks closely at the chart. “Isn’t this Mr. Smith, in for a hemorrhoidectomy?”
As he realizes what his father had done, Lamont grins. “Yes. Yes, he is.” They haul Fred away, and the show cuts to a commercial.
I immediately also thought of The Simpsons, but a different (and earlier I think) episode. The one where Skinner gets fired because of a prank Bart pulls while Superintendent Chalmers is there. Before that happens Skinner has locked up Bart, Nelson & the bullies in the basement, made sure the school is extra tidy etc. At one point Chalmers passes under a big banner welcoming him to the school and Chalmers calls it, “Transparent toadying” to which Skinner hurriedly says, “It was the children’s idea, I tried to stop them!” and Chalmers says, “It’s always the children’s fault isn’t it Seymour?” to which Skinner smugly replies, “Yes, yes it is”.
Really, really great episode from the golden days of the series…
They’re from about the same time. You’re quoting a line from “Whacking Day,” which was from late in season four, and bouv is talking about “Homer’s Barbershop Quartet,” which was produced at the end of season four and aired as the premiere of season five.
I know what the OP means. It has to be deadpanned.
I totally associate it with The Simpsons.
I immediately thought of this:
Close, but he doesn’t repeat “Yes.”
Perhaps I am thinking of The Simpsons, Labrador et al.
One of the Airplane! movies?
I wouldn’t be surprised if you could find it in vaudeville.