"troublesome, annoying," 1775, originally in New England dialect, perhaps a dialectal formation from pest (OED compares plaguy "confounded, annoying, disagreeable"). Partridge suggests an origin in Essex dialect. Sometimes in American-English colloquial use a mere intensive, "excessively." Related: Peskily.
a pesky mosquito
perversity
pervert
perverted
pervious
peseta
pesky
peso
pessary
pessimism
pessimist
pessimistic