Etymology
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Words related to *wegh-

always (adv.)
mid-14c., contraction of Old English phrase ealne weg "all the time; quite, perpetually," literally "all the way," with accusative of space or distance, though the oldest recorded usages refer to time; see all + way (n.). The adverbial genitive -s appeared early 13c., was rare before c. 1400, but is now standard, though the variant alway survived into 1800s. Meaning "every time" is from early 13c.
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away (adv.)
late Old English aweg, earlier on weg "on from this (that) place;" see a- (1) + way (n.).

Meaning "from one's own or accustomed place" is from c. 1300; that of "from one state or condition to another" is from mid-14c.; that of "from one's possession (give away, throw away) is from c. 1400. Colloquial use for "without delay" (fire away, also right away) is from earlier sense of "onward in time" (16c.). Meaning "at such a distance" (a mile away) is by 1712. Intensive use (as in away back) is American English, attested by 1818. Of sporting events played at the other team's field or court, by 1893.
convection (n.)

1620s, "act of carrying or conveying," from Late Latin convectionem (nominative convectio) "the act of carrying, a carrying or bringing together," noun of action from past-participle stem of Latin convehere "to carry together," from assimilated form of com "with, together" (see con-) + vehere "to carry" (from PIE root *wegh- "to go, move, transport in a vehicle").

Specifically of the transference of heat or electricity through change of position of the heated or electrified body (distinguished from conduction) is from 1834. Related: Convective. Convection current recorded from 1868.

convey (v.)

early 14c., conveien, "to go along with;" late 14c., "to carry, transport;" from Anglo-French conveier, Old French convoiier "to accompany, escort" (Modern French convoyer), from Vulgar Latin *conviare "to accompany on the way," from assimilated form of Latin com "with, together" (see con-) + via "way, road" (from PIE root *wegh- "to go, move, transport in a vehicle").

Meaning "communicate by transmission" is from late 14c. Sense of "act of transferring property from one person to another" is from 1520s. It was a euphemism for "steal" 15c.-17c., which helped broaden its meaning. Related: Conveyed; conveying.

convex (adj.)

"curved like a circle or sphere when viewed from outside," 1570s, from French convexe, from Latin convexus "vaulted, arched," past participle of convehere "to bring together," from assimilated form of com "with, together," or "thoroughly" (see com-) + vehere "to bring, carry, convey" (from PIE root *wegh- "to go, move, transport in a vehicle").

Possibly the notion is of vaults "carried together" to meet at the point of a roof. Related: Convexity. Convex lens is from 1822.

convoy (n.)

1550s, "the act of guiding or escorting for protection," from obsolete verb convoy "to accompany on the way for protection" (late 14c.), from Old French convoiier, from Vulgar Latin *conviare, literally "go together on the road," from assimilated form of Latin com "with, together" (see con-) + via "way, road" (from PIE root *wegh- "to go, move, transport in a vehicle").

Compare convey. The meaning "an escort, an accompanying and protecting force" is from 1590s; sense transferred by c. 1600 to "train of ships or wagons carrying munitions or provisions in wartime under protection of escort."

deviate (v.)

1630s, "turn aside or wander from the (right) way," from Late Latin deviatus, past participle of deviare "to turn aside, turn out of the way," from Latin phrase de via, from de "off" (see de-) + via "way" (see via). Meaning "take a different course, diverge, differ" is from 1690s. Related: Deviated; deviating. The noun meaning "sexual pervert" is attested from 1912.

devious (adj.)

1590s, "out of the common or direct way," from Latin devius "out of the way, remote, off the main road," from de via; from de "off" (see de-) + via "way, road" (see via). Compare deviate. Originally in the Latin literal sense; the figurative sense of "deceitful" is first recorded 1630s. Related: Deviously; deviousness. Figurative senses of the Latin word were "retired, sequestered, wandering in the byways, foolish, inconsistent."

envoy (n.)
"messenger," 1660s, from French envoyé "messenger; a message; a sending; the postscript of a poem," literally "one sent" (12c.), noun use of past participle of envoyer "send," from Vulgar Latin *inviare "send on one's way," from Latin in "on" (from PIE root *en "in") + via "road" (see via (adv.)). The same French word was borrowed in Middle English as envoi in the sense "stanza of a poem 'sending it off' to find readers" (late 14c.).
evection (n.)

1650s, "act of carrying out or away," from Late Latin evectionem (nominative evectio) "a carrying upward, a flight," from Latin evehere, from assimilated form of ex "out of, from within" (see ex-) + vehere "to carry" (from PIE root *wegh- "to go, move, transport in a vehicle"). Astronomy sense, "second lunar inequality,"  is from 1706.