Dialectal or archaic form of 'with'.
From Old English mid (with), which is an older form than the 'with' that became standard. Different English dialects preserved different Old English prepositions for centuries.
Words like 'wid' show that English dialects aren't new mistakes—they're survivors of Old English that one group of speakers kept while most others switched to 'with,' showing how language change isn't about one way being 'right.'
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