Present participle of cheap (archaic); making something cheap or reducing its price (rarely used modern form).
Cheap plus -ing. This is an archaic or rare formation since 'cheapen' is the standard modern verb; 'cheaping' represents an older pattern of making verbs directly from adjectives.
Old English readily formed verbs by adding -ian to adjectives (like 'whit' becoming 'whiten'), and 'cheaping' is a ghost of that system—most such forms died out, which is why it sounds archaic to modern ears.
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