1550s, Doll, an endearing name for a female pet or a mistress, from the familiar form of the fem. proper name Dorothy (q.v.). The -l- for -r- substitution in nicknames is common in English: compare Hal for Harold, Moll for Mary, Sally for Sarah, etc.
From 1610s in old slang in a general sense of "sweetheart, mistress, paramour;" by 1640s it had degenerated to "slattern." Sense of "a child's toy baby" is by 1700. Transferred back to living beings by 1778 in the sense of "pretty, silly woman." By mid-20c. it had come full circle and was used again in slang as an endearing or patronizing name for a young woman.
1867, in dialect, "to pet, indulge" (a child), from doll (n.). Usually with up. Meaning "to dress (up)" is by 1906, American English. Related: Dolled; dolling.
Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."
As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.
1550s, "to drive and catch (swans)," from up (adv.). Intransitive meaning "get up, rise to one's feet" (as in up and leave) is recorded from 1640s. Sense of "to move upward" is recorded from 1737. Meaning "increase" (as in up the price of oil) is attested from 1915. Compare Old English verb uppian "to rise up, swell." Related: Upped; upping. Upping block, used for mounting or dismounting horses, carriages, etc., is attested from 1796 (earlier was horsing-block, 1660s).