Etymology
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much (adj.)

c. 1200, "great in quantity or extent" (also "great in size, big, large," a sense now obsolete), a worn-down form (by loss of unaccented last syllable) of Middle English muchel "large, tall; many, in a large amount; great, formidable," from Old English micel "great in amount or extent," from Proto-Germanic *mekilaz, from PIE root *meg- "great."

As a noun, "a large quantity, a great deal," and as an adverb, "in a great degree, intensely, extensively," from c. 1200. Since 17c. the adverb has been much-used as a prefix to participial forms to make compound adjectives. For vowel evolution, see bury. Too much was used from late 14c. in the senses "astonishing, incredible," also "too offensive, unforgivable." Much-what "various things, this and that" (late 14c.) was "Very common in the 17th c." [OED] and turns up in an 1899 book of Virginia folk-speech as well as "Ulysses."

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obliged (adj.)

"bound by ties of gratitude," 1540s, past-participle adjective from oblige. Earlier it meant "be in bondage, be bound by (a promise, pledge, rule, etc.)," also "be liable for the payment of; be condemned" (mid-14c.).

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must (v.)

auxiliary of prediction, "be obliged, be necessarily impelled," from Old English moste, past tense of motan "have to, be able to," from Proto-Germanic *motanan (source also of Old Saxon motan "to be obliged to, have to," Old Frisian mota, Middle Low German moten, Dutch moeten, German müssen "to be obliged to," Gothic gamotan "to have room to, to be able to"), perhaps from PIE root *med- "take appropriate measures," but this old suggestion lately has been doubted. Used as present tense from c. 1300, eventually displacing motan, from the custom of using past subjunctive as a moderate or polite form of the present.

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beholden (adj.)
"under obligation, obliged, bound in gratitude," mid-14c., originally past participle of behold (and preserving the original past participle of hold), but a sense directly related to this usage is not recorded among the many and varied meanings attested for behold.
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walk-over (n.)
"easy victory," 1838, such as one that happens in the absence of competitors, when the solitary starter, being obliged to complete the event, can traverse the course at a walk. Transferred sense of "anything accomplished with great ease" is attested from 1902. To walk (all) over (someone) "treat with contempt" is from 1851.
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muchly (adv.)

"greatly, much," 1620s, from much + -ly (2). Now obsolete or slang. Middle English simply used much as an adverb.

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coveted (adj.)

"much-desired, much sought-after," by 1875, past-participle adjective from covet (v.).

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polymath (n.)

"person of various learning," 1620s, from Greek polymathēs "having learned much, knowing much," from polys "much" (from PIE root *pele- (1) "to fill") + root of manthanein "to learn" (from PIE root *mendh- "to learn"). Related: Polymathy "acquaintance with many branches of learning" (1640s, from Greek polymathia "much learning"); polymathic.

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multi- 

before vowels mult-, word-forming element meaning "many, many times, much," from combining form of Latin multus "much, many," from PIE *ml-to-, from root *mel- (2) "strong, great, numerous." It was much-used in forming Latin compounds in classical times and after (such as multianimis "having much courage," multibibus "much-drinking," multicomus "having much hair," multiloquus "talkative"). Many English words that use it (multinational, etc.) are 20c. coinages.

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multiloquent (adj.)

"speaking much, very talkative," 1650s; from Latin multi- "much" (see multi-) +  loqui "to speak" (from PIE root *tolkw- "to speak").

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