Dialectal or specialized term; possibly related to 'bane' (harm) or to regional blacksmithing/metalwork processes involving heating.
Potentially from 'bane' (Old English 'bana,' meaning harm or death) with '-ing' gerund suffix, or from specialized craft terminology not fully documented in standard dictionaries.
Some words are poorly documented because they're so specialized—if 'baining' is a metalworking term, it might exist only in regional craft traditions, making it a window into lost occupational knowledge.
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