The word asperity traces back to Latin.  The root adjective asper meant "rough, uneven, harsh, or bitter" (used for bad weather, sour wine, or hard times).  It formed the noun asperitas (genitive asperitatem), meaning "roughness, unevenness, or severity".  The term passed into Old French and Anglo-French as asperité or aspreté (modern French âpreté), meaning "difficulty, hardship, or harsh treatment". 

According to the Oxford English Dictionary (OED), the earliest known use of the noun "asperity" in English is from around 1225 in the Middle English religious guide [Ancrene Riwle] (also spelled Ancrene Wisse).  It was initially used in the abstract sense of "hardship" or a painful situation.  By the 15th century, the spelling and direct form of the English word shifted closer to the original Latin asperitatem (asperity).  The literal physical meaning ("roughness of a surface") appeared in the early 1400s, while the modern figurative meaning ("harshness of tone or temper") became common by the 1660s.  

The related word exasperate was first used in English in 1534 as a verb, found in a letter written by Thomas More.  The adjective form appeared slightly later in the mid-1500s (recorded around 1540).  

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ASPERITY Definition & Meaning - Merriam-Webster

ASPERITY Synonyms: 140 Similar and Opposite Words | Merriam-Webster Thesaurus

ASPERITY Related Words - Merriam-Webster