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Old English bolla "bowl, cup, pot," merged with Middle Dutch bolle "round object," borrowed 13c., both from Proto-Germanic *bul-, from PIE *bhel- (2) "to blow, inflate, swell" (see bole). Influenced in meaning by Latin bulla "bubble, ball," ultimately from the same PIE root. Extended c.1500 to "round seed pod of flax or cotton." Boll weevil is 1895, American English.
In south Texas, among Spanish-speaking people, the insect is generally known as the 'picudo,' a descriptive name which refers to the snout or beak of the insect. English-speaking planters generally referred to the insect at first as 'the sharpshooter,' a term which for many years has been applied to any insect which causes through its punctures the shedding of the squares or the rotting of the bolls. As there are several native insects that are commonly called sharpshooters and which, though injurious, are by no means to be compared with this insect, it becomes necessary to discourage in every way the use of the word sharpshooter as applied to this weevil. The adoption of the term 'Mexican cotton-boll weevil' for the new pest is recommended. [New Mexico College of Agriculture and the Mechanic Arts Agricultural Experiment Station Bulletin No. 19, April 1896]A case of entomology meddling in etymology.