The process of attaching or working with heels on shoes, or the act of tilting something to one side.
From Old English 'hǽl' meaning heel, combined with the suffix '-ing' to indicate an action or process. The word evolved to describe both the craftsmanship of heel attachment and the physical action of tilting.
Naval sailors use 'heeling' to describe a ship tilting in the wind—the same word describes your shoe repair! This shows how everyday craftspeople's language becomes part of maritime terminology.
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