Old English ceowan "to bite, gnaw, chew," from West Germanic *keuwwan (source also of Middle Low German keuwen, Dutch kauwen, Old High German kiuwan, German kauen), perhaps from PIE *gyeu- "to chew" (source also of Old Church Slavonic živo "to chew," Lithuanian žiaunos "jaws," Persian javidan "to chew").
Figurative sense of "to think over" is from late 14c.; to chew the rag "discusss some matter" is from 1885, apparently originally British army slang. Related: Chewed; chewing. To chew (someone) out (1948) probably is military slang from World War II. Chewing-gum is by 1843, American English, originally hardened secretions of the spruce tree.
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).