"tiny, dainty, miniature," 1905, from childish pronunciation of sweet (adj.). Compare tummy from stomach.
Entries linking to twee
Old English swete "pleasing to the senses, mind or feelings; having a pleasant disposition," from Proto-Germanic *swotja- (source also of Old Saxon swoti, Old Frisian swet, Swedish söt, Danish sød, Middle Dutch soete, Dutch zoet, Old High German swuozi, German süß), from PIE root *swād- "sweet, pleasant" (Sanskrit svadus "sweet;" Greek hedys "sweet, pleasant, agreeable," hedone "pleasure;" Latin suavis "pleasant" (not especially of taste), suadere "to advise," properly "to make something pleasant to"). Words for "sweet" in Indo-European languages typically are used for other sense as well and in general for "pleasing."
Then come kiss me, sweet-and-twenty!
Youth's a stuff will not endure.
Also "being in a sound or wholesome state" (mid-13c.), and, of water, "fresh, not salt" (late Old English). As an intensifier from 1958. Sweet in bed (c. 1300) was the equivalent of modern "good in bed." To be sweet on someone is first recorded 1690s. Sweet sixteen first recorded 1767. Sweet dreams as a parting to one going to sleep is attested from 1897, short for sweet dreams to you, etc. Sweet-and-sour in cookery is from 1723 and not originally of oriental food. Sweet nothings "sentimental trivialities" is from 1900. Sweet spot is from 1976, first in reference to tennis rackets. Sweet corn is from 1640s.