Middle English stonden, standen, from Old English standan "occupy a place; stand firm; congeal; stay, continue, abide; be valid, take place; oppose, resist attack; stand up, be on one's feet; consist, amount to" (class VI strong verb; past tense stod, past participle standen).
This is from Proto-Germanic *standanan, source also of Old Norse standa, Old Saxon standan, Old Frisian stonda, Gothic standan, Old High German stantan, which are related to simpler forms, such as Swedish stå, Dutch staan, also German stehen, with vowel perhaps altered by influence of gehen "go"), ultimately from PIE root *sta- "to stand, make or be firm."
The sense of "exist, be present" is attested from c. 1300. The meaning "to cost" is from mid-14c. (for sense, compare cost (v.), from Latin constare, literally "to stand at"). The meaning "be so high when standing" is from 1831.
The meaning "encounter without flinching or retreating" is from 1590s; that of "endure successfully, undergo, come through" is from c. 1600. The weaker sense of "put up with" is attested by 1620s (to not stand it is by 1750).
The meaning "submit" (to chances, etc.) is from c. 1700. The meaning "pay for as a treat" is from 1821. The sense of "become a candidate for office" is from 1550s. Nautical sense of "hold a course at sea" is from 1620s.
Stand back "keep (one's) distance" is from late 14c. To stand down is from 1680s, originally of witnesses in court; in the military sense of "come off duty" it is by 1916. To stand one's ground is by 1620s; to stand one's chances is by 1725.
Phrase stand pat (1869) is from poker, "declare one's intention to play one's hand as dealt," also figurative, earlier simply stand (1824 in other card games).
The phrase stand to reason (1620) "be reasonable; be natural, evident, or certain," is from earlier stands with reason; the notion in the verb is "adheres to, conforms with."
To let (something) stand is from c. 1200. The construction stand and (deliver, etc.) was in late Old English in Biblical translations.
