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.