Does Middle English "w" relate to "uȝ"?
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What you have underlined in the image is just a letter "w". In old handwriting, "w" is sometimes rather elaborate, with curls or twists. See the examples at the bottom left of page 5 in this document for other similar ws: Old English Paleography", by Helen E. "Jean" Cruickshank, or the example on this page: 16th Century Document Hand.
The curl on the right of this w has nothing to do with the letter ȝ (yogh). It's just a coincidence that w in this hand somewhat resembles uȝ. The word shown is definitely written what, not uȝat.
Because of sound changes, some words such as plow did show variation between w and uȝ (also uh, ugh, wȝ, wh, wgh) but that variation is seen after vowels, not at the start of words.