"mad, insane, crazy," especially in love, 1903, perhaps from dip + -y (2), but the exact signification is unclear. Another theory connects it with dipsomania.
Entries linking to dippy
dip v.
Old English dyppan "to plunge or immerse temporarily in water, to baptize by immersion," from Proto-Germanic *daupejanan (source also of Old Norse deypa "to dip," Danish døbe "to baptize," Old Frisian depa, Dutch dopen, German taufen, Gothic daupjan "to baptize"), related to Old English diepan "immerse, dip," and probably a causative of Proto-Germanic *deup- "deep" (see deep (adj.)).
Intransitive sense of "plunge into water or other liquid" and transferred sense "to sink or drop down a short way" are from late 14c. From c. 1600 as "to raise or take up by a dipping action;" from 1660s as "to incline downward;" from 1776 as "to lower and raise (a flag, etc.) as if by immersing."
-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.