Learn English – Variant pronunciation of “obesity”

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It's the result of the same process (that is, erroneous pronunciation) whereby "learn" becomes "larn" in some (very) nonstandard American dialects. One feature of uneducated speech in England around the 1800's was a tendency to pronounce the "er" sound of words like "clerk" as the "ar" sound of "clark". The phenomenon was sufficiently widespread that the English novelist Henry Fielding used pronunciations like "sarvis" for "service", "sartain" for "certain", and "parson" for "person" in the speech of characters meant to seem vulgar or unintelligent. Due to the overwhelming influence of such people in England (that is, the uneducated), these previously unacceptable pronunciations eventually became standard for some words, like Derby, Berkeley, and clerk...
Source(s): J.C. Wells, Accents of English

So a more general sound change that took "er" to "ar" was present in some lower-class British accents when Henry Fielding wrote Tom Jones (ca. 1750). This 1849 dictionary found in Google books indicates that this pronunciation had for the most part vanished a hundred years later¹. The pronunciation now persists in only a handful of words:

Berkeley, clerk, derby, Hertfordshire, sergeant, varsity.

I take the liberty of including varsity here because it was originally short for university. However, university has reverted to the standard pronunciation, while varsity has switched to the phonetic spelling.

¹ Interestingly, the dictionary also says that many Americans pronounced sergeant with "er".

The /ˈɛryən/ pronunciation is just a result of English phonology processing a foreign borrowing that starts with the letters AR.

Aryan is a borrowed word in all languages outside the Indo-Iranian subfamily of Indo-European. The rest of the world pronounces it as some variant of [arjan], which comes, as noted, from Sanskrit ārya /a:ryə/ 'compatriot'. Therefore, /'aryən/ is a perfectly acceptable English pronunciation, and the only acceptable one when using the term in its modern Indian sense.

Any use of Aryan (outside scare quotes) that refers to Germany or white racism is a result of romantic interpretations of 19th century German linguistic scholarship (e.g, Grimm's Law), which unearthed the prehistory of the "Indo-Germanic" (as I-E was then called, from names of its Eastern- and Westernmost families) languages. It was all very exciting, apparently. See also Wagner, Mad King Ludwig, Neuschwanstein, German Empire.

The AHD of IER says that Skt ārya comes from the PIE root *aryo- 'Self-designation of the Indo-Iranians'; other descendants of the same root are Iran and, surprisingly, Eire -- Celtic languages sometimes retain PIE roots that are otherwise lost in the Centum group.

None of these are English words, and so English treats them the same way it treats all borrowed words -- it changes the pronunciation until it tastes right. That's all.

Edit:

I almost forgot, another reason to pronounce Aryan /'aryən/ is because Arian /'ɛriən/ usually refers to Arianism, a very important variety of Christianity that was the religion of the Ostrogoths in Italy, and the Visigoths in Spain. The only Gothic texts known to exist are translations of various parts of the (Arian Christian) New Testament.