Why is the past tense of may, might? When you see other past forms of auxiliary verbs, they usually have -ould, like should, could, and would. Unlike other forms, the past tense of may is might not mought.
With the German forms mögen (infinitive), er mag ( he may), er mochte/er möchte (he might) you may get an idea about historical sound changes. The German stem mag/mög has a regular past with -te, but g changes to ch, which is easier to speak before t.
In English g vanishes, but y in may reminds us that there was a g. English might is parallel to German mochte/möchte. But in English the g-sound vanishes and only the spelling gh is a hint at the original g-sound.
Summary: It's not clear to me whether "might" evolved regularly or irregularly as a form of "may". If it was regular, I don't know the rules, and if it was irregular, I haven't identified a clear motivating factor. But it seems to be related both to the vowel originally being "a", and the consonant /h/ that existed in older forms of this word.
The Oxford English Dictionary (OED) entry for "may" backs up what user3847 says about "mought" existing historically and dialectally:
Forms with -u- in the present indicative plural, present subjunctive, and past tense (see Forms senses 2c γ. forms, 3 γ. forms, and 4d) are recorded in Old English only in a few late texts, but the existence of forms with a back vowel in Old Frisian, Old Saxon, and Old High German suggests that similar forms may have occurred in West Germanic and have been transmitted to varieties of Old English other than those exemplified in the major documents. Since the present tense forms were morphologically originally past tense, it seems possible that this alternation between -u- in the present indicative plural and subjunctive, and West Germanic -a- (Old English -æ-/-a-) in the other present forms arose by analogy, perhaps with the preterite-present verb shall, in which, in Old English and virtually all the other Germanic languages, the similar vowel alternation reflected Indo-European ablaut. The back vowel spread to the infinitive and present participle in many dialects of Middle English.
The Old English past tense variant with -u- is attested late and only rarely (e.g. in the Laud MS of the Anglo-Saxon Chron.), but gave rise to numerous Middle English forms. The early modern English reflex mought, containing, according to Laneham's transcription (1575), the same vowel as such words as out, had an extensive literary currency in the 16th and 17th cent.
Wikipedia shows the Proto-Germanic (PG) ancestor *maganą as having the vowel "a" in the first syllable in all of its forms. The spirantization of "g" to "h" already occurs here, though. For some reason I don't understand, the vowel changed to "u" or "o" in some descendants such as German.
The OED lists forms like
mæht (Northumbrian), OE meaht, OE meht (Kentish), OE–ME miht, eME mahht (Ormulum), ME maht, ME maiȝt, ME mait, ME mat, ME mate, ME maucht, ME mayht, ME mayhte, ME mayt, ME mayth, ME meiht, ME micht, ME miȝt, ME mikt, ME mith, ME myȝt, ME myȝte, ME myht.
To me, it looks like the following steps occurred:
For reasons that are unclear to me, "a" was fronted to an æ-like vowel (æ/ea/e).
This æ-like front vowel eventually caused the following "h/gh" consonant to be realized as the front allophone [ç]
under the influence of the following sound [ç], the æ-like front vowel was raised and lengthened to (pre-Great Vowel Shift) [iː]; sometime during or after this process the [ç] was lost. (Lengthening before [ç] is a well-known Middle English sound change seen in many other words such as sight < PG *sihtiz, wight < PG *wihtiz, flight < PG *fluhtiz.)
subsequently, this changed just like other [iː] according to the Great Vowel Shift to become modern English /aɪ/
Less extreme examples of front vowels being raised to pre-Great Vowel Shift [iː] before [ç] are seen in the words
nigh < PG *nēhw; PG *ē usually became Old English ē or ǣ > ME /eː/ or /ɛː/ (respectively) > ModE /iː/ (both)
high < PG *hauhaz (according to Wiktionary); PG *au usually became OE ēa > ME /ɛː/ > ModE /iː/
Mought is actually an alternative, obsolete or dialectical form of might. Examples appear in Old English texts but it is obsolete, somehow morphing into 'might'. 'Mought' can still be heard today in regional USA dialects (South Middle USA). South Middle USA is a long way of saying 'Appalachia' where some old English words have survived in communities isolated in mountain valleys. I once heard the word 'roots' pronounced as 'ruts' by a woman from Appalachia. I heard this woman in the early 1950s in New York. But the expansion of TV reception, has probably all but wiped out the remnants of Old English. Here's an example: '...Queen Elizabeth of England, with bills to sign, but he would always first put her into some discourse of estate, that she mought the less mind the bills.' For more examples see wordnik.com