Middle English holden, earlier halden, from Old English haldan (Anglian), healdan (West Saxon), "to contain; to grasp; to retain (liquid, etc.); to observe, fulfill (a custom, etc.); to have as one's own; to have in mind (of opinions, etc.); to possess, control, rule; to detain, lock up; to foster, cherish, keep watch over; to continue in existence or action; to keep back from action," class VII strong verb (past tense heold, past participle healden), from Proto-Germanic *haldanan (source also of Old Saxon haldan, Old Frisian halda, Old Norse halda, Dutch houden, German halten "to hold," Gothic haldan "to tend").
Based on the Gothic sense (also present as a secondary sense in Old English), the verb is presumed originally in Germanic to have meant "to keep, tend, watch over" (as grazing cattle), later "to have." Ancestral sense is preserved in behold. The original past participle holden was replaced by held beginning 16c., but survives in some legal jargon and in beholden.
The modern use in the sense "lock up, keep in custody" is from 1903. Hold back in the figurative senses is from 1530s (transitive); 1570s (intransitive). To hold off is early 15c. (transitive), c. 1600 (intransitive). Hold on is early 13c. as "to maintain one's course," 1830 as "to keep one's grip on something," 1846 as an order to wait or stop.
To hold (one's) tongue "be silent" is from c. 1300. To hold (one's) own is from early 14c. To hold (someone's) hand in the figurative sense of "give moral support" is from 1935. To hold (one's) horses "be patient" is from 1842, American English; the notion is of keeping a tight grip on the reins. To have and to hold have been paired alliteratively at least since c. 1200, originally of marriage but also of real estate. To hold water in the figurative sense "be sound or consistent throughout" is from 1620s.
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).