Bow vs Bow - etymology of the differing pronunciation

Solution 1:

Even if the words come from words where the base form is the same, they seem to come from different forms of that word. On dictionary.com you can see different forms in the etymology:

For the verb:

before 900; Middle English bowen (v.), Old English būgan; cognate with Dutch buigen; akin to German biegen, Gothic biugan, Old Norse buga, etc.

And for the noun:

before 1000; Middle English bowe (noun), Old English boga; cognate with Dutch boog, German Bogen, Old Norse bogi; akin to bow

So, it seems that the difference was there already when the words were introduced in English. I don't know why they are spelled the same in Modern English, though. Most other languages seem to have diffent spellings for the words, for example Swedish buga for the verb and båge for the noun.