What's the Source for Jerusalem and Sepphoris Having Larger Measuring Units?

Question

In Rabbi Pinchas Kehati's introduction to Masekhet Challah, and again in his commentary on Eduyyot 1:2, reference is made to the adjusting of measurements when the Jews "arrived at" Jerusalem, and again when they "arrived at" Sepphoris. In both instances, the measuring tools were increased in size by one sixth, such that the measurement for an 'omer in the wilderness (given as 1/10th of an ephah in Exodus 16:36) required 1.5 qavim instead of 1.8, and subsequently 1.25.

Seeing as neither masekhta (Challah nor Eduyyot) has gemara in the Bavli, and seeing as R' Kehati, in neither of these instances, has named his sources, can anybody please provide me with the origin of this tradition? Eduyyot 1:2 mentions the changing of the measurements, but it doesn't say where, and interpreting that mishna requires of us to suggest that it is speaking of the second adjustment and not the first.

What is the origin of this tradition? Why did they change the measurements? And what does it mean when we speak of them "arriving" in Jerusalem and Sepphoris (Tzippori)?

For those who are interested, and who don't otherwise have access to it, the following is R' Kehati's language (from the introduction to Challah):

האיפה היא 18 קב, ונמצאת עיסת מדבר החייבת בחלה 1.8 קב. ברם, כשבאו לירושלים הגדילו את המידות בשישית, כלומר שכל מידה מדברית נעשתה 5/6 של המידה הירושלמית, ומכאן - "עשירית האיפה" במידה הירושלמית היא קב ומחצה... ומשהגדילו המידות פעם שנייה בצפורי, שהגדילו שם המידה הרושלמית בששית, אמרו חכמים: "חמשת רבעים חייבים", כלומר שעיסה העשויה מחמשת רבעי הקב קמח... חייבת בחלה

Answer 1

Regarding the measurements, there is a long discussion in the Tlmud Bavli, Eruvin 83(p1-2). At the end (p2), the Talmud says that the Challah measure is 7 quarters of flour = 6 quarters of Jerusalem = 5 quarters of Sepphoris.

Notice that the Talmud doesn't say here anything about the reasons or the meaning.

תנו רבנן (במדבר טו) ראשית עריסותיכם כדי עיסותיכם וכמה עיסותיכם כדי עיסת המדבר וכמה עיסת המדבר דכתיב (שמות טז) והעומר עשירית האיפה הוא מכאן אמרו ז' רבעים קמח ועוד חייבת בחלה שהן ו' של ירושלמית שהן ה' של ציפורי מכאן אמרו האוכל כמדה זו ה"ז בריא ומבורך יתר על כן רעבתן פחות מכאן מקולקל במעיו

(תלמוד בבלי, עירובין דף פ"ג ע"א-ע"ב)

Answer 2

I seem to have hit something of a brick wall with this, though may have enough information now to tentatively answer my own question. It seems that this phenomenon is alluded to in a number of places: in addition to those I mentioned in the question, mChallah 2:6, bEruvin 83a-b (thanks, Moti, for your answer), bShabbat 15a, bShabbat 76b, bPesachim 48b, etc. In addition to that, the three commentaries that have been of the most assistance in tracking down the earliest form of this tradition are Tosafot (Eruvin 83b, s.v. שבעת רבעים), Tosafot Yom-Tov (Challah 1:4, s.v. ופחות מחמשת רבעים) and the Kessef Mishna (MT, Hilkhot Bikkurim 6:15). Those who are interested in following this further should look at those.

Now that I've looked at each of these passages, it seems to me that the oldest text amongst them is the beraita in Eruvin 83a (my translation):

ת"ר סאה ירושלמית יתירה על מדברית שתות ושל צפורית יתירה על ירושלמית שתות נמצאת של צפורית יתירה על מדברית שליש

The rabbis taught: A seah in Jerusalem is one sixth larger than a wilderness [seah], and [a seah] of Sepphoris is one sixth larger than a Jerusalem [seah], meaning that [a seah] of Sepphoris is one third larger than a wilderness [seah].

Note that this beraita is not mentioned in Sifrei on Bemidbar 15, nor in the Mekhilta on Shemot 16. Those two texts both appear to assume that there is one standard measurement for measuring out an 'omer, and show no awareness of the differences between Jerusalem and Sepphoris. If this beraita has a source elsewhere in the midrash halakha, or even in the Tosefta, I don't know what it is.