1590s, "act of putting on vestments" (a sense now found in investiture); later "act of being invested with an office, right, endowment, etc." (1640s); and "surrounding and besieging" of a military target (1811); from invest + -ment.
Commercial sense of "an investing of money or capital" is from 1610s, originally in reference to the East India Company; general use is from 1740 in the sense of "conversion of money to property in hopes of profit," and by 1837 in the sense "amount of money invested." For evolution of the commercial senses, see invest.
1510s, "action of besieging" (a sense now obsolete), from French obsession and directly from Latin obsessionem (nominative obsessio) "siege, blockade, a blocking up," noun of action from past-participle stem of obsidere "to besiege" (see obsess). Later (c. 1600), "hostile action of an evil spirit" (like possession but without the spirit actually inhabiting the body). Transferred sense of "action of anything which engrosses the mind" is from 1670s. Psychological sense "idea or image that intrudes on the mind of a person against his will" is from 1901.
early 13c., segge, "a seat, chair, stool; ceremonial seat of a king," senses now obsolete, from Old French siege, sege "seat, throne," from Vulgar Latin *sedicum "seat," from Latin sedere "to sit" (from PIE root *sed- (1) "to sit").
The military sense, "the stationing of an attacking force before or around a fortified place; the act or process of besieging a city, castle, etc." is attested from c. 1300; the notion is of an army "sitting down" before a place.
The oldest sense preserved in archaic Siege Perilous (early 13c.), the vacant seat at Arthur's Round Table, according to prophecy to be occupied safely only by the knight destined to find the Grail. Also in Middle English "a privy, a latrine, chamber pot" (c. 1400), hence in 16c. "excrement, fecal matter; the anus."
c. 1200, "short, loose, sleeveless cloak," variant of mantle (q.v.). Sense of "movable shelter for soldiers besieging a fort" is from 1520s.
The meaning "timber or stone supporting masonry above a fireplace" is attested by 1510s; it is a shortened form of Middle English mantiltre "mantle-tree" (late 15c.) "beam of oak or some other hard wood above a fireplace or oven" (with tree in the now-obsolete sense of "beam"). But the exact meaning of mantle in that had become obscure by the 19c.
In a fire-place, the mantle or mantlepiece, may have been either a covered or chimney-piece; or the part below it to which a hanging, for the sake of making a flue for the wind to draw up the fire, was attached. The details, however, of this are uncertain. [Robert Gordon Latham, "A Dictionary of the English Language," 1882]
Mantel-clock "clock intended to sit on a mantle-shelf," is by 1824.