I saw the word mighty today (not a word you see all the time these days), and immediately wondered if it were linked to the modal verb might (as in I might be mighty, but might I be the mightiest?)
I’ve trained myself to be wary of any apparent patterns when it comes to language, because languages evolve so haphazardly that any apparent links between words are often just coincidences.
But I felt I was on to something in this case, because of the specificity of the spelling.
And of course there is a link, and it’s pretty logical too. Might comes from the Proto-Germanic *makhti-, meaning to be able, power. This became may in English, with might originally having been the past form of may.
Equally, might developed into a noun, meaning ability or power. The meaning of this word gradually became more specialised and came to mean power more than basic ability, and then came to specifically mean great strength.
And that’s why the lowly might and the… mighty…. might are identical!