Those familiar with William Shakespeare's history play Henry IV may recall how the portly Falstaff remembered the thin Justice Shallow "like a man made after supper of a cheese-paring." Falstaff's unusual food simile is one not easily forgotten, and people began to associate cheese-parings (bits of cheese trimmed off a larger portion) with other things of little significance and value. In the 19th century, the meaning of cheeseparing was extended to "miserly economizing." (Presumably, the practice of paring off the rind so as to waste the minimum of cheese was viewed as an excessive form of frugality.)
Ebenezer Scrooge is portrayed as a taskmaster so dedicated to cheeseparing that he would prefer that his employees freeze to death rather than splurge on heat.