1859, "abounding in shrimp," from shrimp (n.) + -y (2). Also "small, slender, and weak." An earlier adjective was shrimpish (1540s).
Entries linking to shrimpy
shrimp n.
early 14c., "slender, long-tailed, ten-footed, edible marine crustacean," Middle English shrimpe, probably from or related to Old Norse skreppa "thin person," from Proto-Germanic *skrimp- (see scrimp). This is related to Old English scrimman "to shrink."
The connecting notion between the two senses would be probably "thinness" (compare Danish dialectal skrimpe "thin cattle"). OED speculates that the general sense of "shrunken creature, puny person" is probably directly from the etymological source, however that meaning in English is attested only from late 14c. and is felt as transferred from the crustacean sense. An especially puny one might be a shrimplet (1680s). Shrimp cocktail is attested by 1937.
-y 2
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.