A “cheveril glove” is another term for a kid glove.
“Here’s a wit of cheverel, that stretches From an inch narrow to an ell broad!” (Romeo and Juliet)
“The Fabric’s The Thing: Literal and Figurative References to Textiles in Selected Plays of William Shakespeare“ by Nancy J. Owens and Alan C. Harris tells us: “Cheveril or cheverel was kid leather noted for its elasticity and ability to be stretched.” They continue to expand on the above quote from Romeo and Juliet, writing, “Thus, in a heavy bout of word play, we have a joking yet admiring commentary on Romeo’s broad sense of humor and ability to pun.”
“A plague of opinion! a man may wear it on both sides, like a leather jerkin.” (Troilus and Cressida)
Ownens and Harris expand on the quotation from Trolius and Cressida above. “The use of leather…is a fairly transparent metaphor based upon the almost trivial observation that leather could be worn on either side. Thus, ‘a plague of opinion; implies that, depending on the source and the situation, one could have either a good or a bad reputation.
Clown: ”You have said, sir. To see this age! A sentence is but a cheveril glove to a good wit: how quickly the wrong side may be turned outward!” (Twelfth Night)
We see echoes of references to cheveril’s ability to be worn on either side/turned inward or outward in Twelfth Night as well, when the clown references “good wit” and how it can quickly be “turned outward.”
In John H. Brittain’s Twelfth Night, Or, what You Will, a footnote gives us more insight into the meaning behind the Clown’s invocation of the term “cheveril” in this particular instance:
“The clown gives need expression to the truth that ta sentence may often be made to bear a meaning entirely opposite to that which was intended. Such is the case only when the sentence contains some ambitious term or phrase.”