To coat, cover, or sweeten something with sugar.
From prefix 'be-' (to cause to be) + 'sugar' (from Arabic 'qandi'). The 'be-' prefix became productive in Middle English for creating verbs meaning to cover or treat with something.
This word exemplifies how English used to create new verbs freely using 'be-' — you could 'be-' almost any noun to mean 'to cover with it.' Most of these words died out, but 'besmirch' and 'begrudge' survived because they were used frequently enough.
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