Early examples of the expression from transcripts
The phrase "the reason being is that..." appears in Google Books search results going back to the late 1960s—initially in reports of hearings and other spoken-word contexts. Here are the five earliest Google Books matches that came up in a series of searches that I ran.
From Journal of the House of Representatives of the State of Michigan, volume 2 (1968) [snippet view]:
...the heart of the civil rights operation and as I've indicated on this floor before that Michigan is proud of its record in terms of one of the few states to have written a section in the constitution that provides for civil rights and its protection. But today, again on this floor, this Legislature has seen fit not to increase and not to enlarge on this eve increasing sea of problems. The other reason being is that I think this is what I call good crime legislation. All the crime bills that we've had before and are still pending is of little value, but this kind of legislation can go a long ways in preventing the kind of holocaust that we ...
From Kenya National Assembly, Official Report, volume 17, issue 1 (1969) [snippet view]:
Mr. G. G. Kariuki: Mr. Speaker, the reason being is that I remember we took a unanimous decision at the Parliamentary Group, and now, Mr. Speaker, it seems as if Members did not wholeheartedly support what we agreed at the Parliamentary Group meeting.
From Records of the Louisiana Constitutional Convention of 1973: Convention Transcripts (1974) [combined snippets]:
On tax issues our committee has taken the stand that they require two-thirds vote. I support that. The reason being is that tax issues are so vital and so important that we should neither give exemptions nor take them away without a clear....clear mandate from all sections of the state. I'm afraid that with a simple majority, we might get a semi-mandate....a quasi mandate, or pseudo mandate, and do something that would harm a large part of this state.
Mr. Roemer I'm glad you brought that point up. You're absolutely correct. If we were to...if we were to attempt to reverse that law that passed, like you say, '71—which I hope someday the legislature will—it would be a tremendous pressure lobby here not to. The reason being is that the income tax collection would be cut by some forty percent, Woody, and this revenue sharing fund would suffer. I don't want to see that happen.
"Mr. Roemer" in the second excerpt above is Buddy Roemer, who later served in the U.S. House of Representatives and later still was elected governor of Louisiana.
From U.S. House of Representatives, Synthetic Fuel Oversight Hearing: Hearing Before the Subcommittee on Economic Stabilization of the Committee on Banking, Finance, and Urban Affairs (March 3, 1981) [combined snippets]:
in the neighborhood of $500 or $600 billion in Federal credit assistance out there right now. Now, I agree, as I indicated in one of the very first things I said to our majority leader here today—and that is that we do need to provide some stimulus and some incentives to the synthetic fuels industry. The reason being is that the Government has so fouled up the marketplace in the last 10 years by artificially—by keeping the price of oil artificially low, that we have destroyed any market for any alternatives.
From Humane Care for Animals in Research: Hearing Before the Subcommittee (1983) [combined snippets]:
Mr. DANNEMEYER [of California]. The reason being is that presumably the Department of Agriculture over the years has established an infrastructure for administering existing law concerning the welfare of animals in this country.
And from Vietnam: A Television History; Legacies; Interview with David Christian, 1983 (July 7, 1983) [Christian was from Bucks County, Pennsylvania]:
As a result, if a man had to balance out, whether he was going to hire a Vietnam veteran, or someone who's the same age and same qualifications, oftentimes the person would take the other, would take the latter, the reason being is because there was no risk. You're asking employers to take a risk and many of the employers were employers that made money off the Vietnam War, would not hire Vietnam veterans.
People ask me on college campuses, they ask me about what it was like to kill a man, and how I felt in killing a man, and I had to tell them that I felt very, very good, and the reason being is that that man was trying to kill me, and that's another concept, uh, a misconception that most people had here, back here, in this world, that we're pathological killers.
It seems quite clear from these examples that the speakers are treating "the reason being" as a set phrase that is synonymous with "the reason." How this understanding came about is a matter for conjecture but it seems to have arisen in multiple places independently, as the 1968 Michigan, 1969 Kenya, and 1973 Louisiana examples suggest.
I should note that most of the speakers quoted above appear to be reasonably well-educated politicians or other public figures. And yet usage of "the reason being is that" does not appear in Google Books search results from a purely written source (as opposed to a transcript) until the 1990s.
Examples of the expression from purely written sources
The first two such Google Books entries are from IEEE Region 10, Institute of Electrical and Electronics Engineers, Victoria [British Columbia] Section, Technology Enabling Tomorrow: Computers, Communications and Automation Towards the 21st Century (1992):
The EES method as described above can be actually used (with some modifications) to estimate the BER of sequential decoders. The key complication is that for practical sequential decoders, the EES method as specified above simply becomes impractical. The reason being is that sequential decoders are often used with long constraint length convolutional codes. For such codes, the error events are quite long.
Computer simulation-based techniques that are based on a Monte Carlo (MC) simulation approach can offer an attractive alternative for simulating optical communications systems. Unfortunate, the evaluation of optical communications systems BER's using a brute-force MC can be extremely difficult, if not impossible. The reason being is that for digital lightwave transmission systems' an error probability ≤ 10-9 is often used as a criterion for satisfactory performance.
and from Darren Dawson, Jun Hu & Timothy Burg, Nonlinear Control of Electric Machinery (1998):
Traditionally, brushed DC (BDC) motors have been used in industrial positioning systems. One reason being is that BDC motors are essentially linear systems and thus easy to control. But in recent years, the development of precision nonlinear controllers has encouraged the use of brushless machines in place of BDC motors.
The most structurally similar expression that I am aware of is the phrase "the thing about it is, is that," which similarly is far more common in spoken English than in written English. However, the latter term yields only two verifiable matches in a Google Books search, whereas "the reason being is that" yields dozens —the vast majority of them from the past 16 years.
Examples of 'the reason being' in different syntactical forms
Apart from the odd but increasingly established set phrase "the reason being is that," the phrase "the reason being" appears in numerous forms that raise no alarms with regard to their acceptability in formal written English. Here are three examples. From a note in Penguin's annotated 1982 edition of Adam Smith The Wealth of Nations, books 1–3:
In Smith's opinion, the labour unit alone was stable, the reason being that the disutility of labour may be said to be constant over time; an argument which serves to remind us that Smith's labour unit is expressed in terms of disutility and not (directly) man hours.
From a letter from E. Lauchli of New York City, dated March 12, 1913, to Engineering News (April 3, 1913):
In Europe, only rock tunnels over two miles long have been and are driven with a top and one bottom heading, the reason being obvious, for the greater the number of headings, the more complicated the driving operations are, and it is only with a first-class organization of men and mining operations, and on long tunnels, that a tunnel can be driven successfully with two headings.
And from Mrinal Kanti Gangopadhyay, Indian Logic in Its Sources on Validity of Inference (1984) [combined snippets, square brackets in original]:
If the former alternative is accepted, the postulation as negating the possibility of the reason being otherwise [i.e. the reason being present even in the absence of the probandum] would have to be applied even to the individual case in respect of which an inference is being resorted to, and by this very postulation the presence of the probandum would be well-established.