Late 18th century: perhaps related to pest.

• pest from Late Middle English:

  At first this was a term for the bubonic plague. It comes via French peste from Latin pestis ‘plague’. Pestilence (Middle English) is from the same root. Pest in the sense of ‘a destructive plant or animal’ is not found until the mid 18th century, when fear of the Black Death has receded. The informal word pesky (late 18th century) may be related to pest perhaps via pesty. Pester (mid 16th century), however, is not directly connected. The source is French empestrer ‘encumber’, but the English form is influenced by pest. Early use included the meanings ‘overcrowd (a place)’ and ‘impede (a person)’. The current sense ‘annoy someone with frequent requests’ is an extension of an earlier use, ‘infest’, referring to vermin. See also plague