[bird's beak] Old English bill "bill, bird's beak," related to bill, a poetic word for a kind of sword (especially one with a hooked blade), from Proto-Germanic *bili-, a word for cutting or chopping weapons (see bill (n.3)). Used also in Middle English of beak-like projections of land (such as Portland Bill).
"financial institution," late 15c., originally "money-dealer's counter or shop," from Old Italian banca and also from French banque (itself from the Italian word), both meaning "table," from a Germanic source (such as Old High German bank "bench, moneylender's table"), from Proto-Germanic *bankiz- "shelf," *bankon- (see bank (n.2)). The etymological notion is of the moneylender's exchange table.
As "institution for receiving and lending money" from 1620s. In games of chance, "the sum of money held by the proprietor or one who plays against the rest," by 1720. Bank holiday is from 1871, though the tradition is as old as the Bank of England. To cry all the way to the bank was coined 1956 by U.S. pianist Liberace, after a Madison Square Garden concert that was panned by critics but packed with patrons.
"natural earthen incline bordering a body of water," c. 1200, from a Scandinavian source such as Old Norse *banki, Old Danish banke "sandbank," from Proto-Germanic *bankon "slope," cognate with *bankiz "shelf" (see bench (n.)). As "rising ground in a sea or rover, shoal," from c. 1600. As "bench for rowers in an ancient galley," 1590s.
There probably was an Old English cognate but it is not attested in surviving documents. The nasalized form likely is a variant of Old Norse bakki "(river) bank, ridge, mound; cloud bank," cognate with Swedish backe, Danish bakke "hill, rising ground."
"to stroke beaks," as doves do, hence, of lovers, "caress fondly," 1590s, from bill (n.2)). Paired with coo at least since 1764; Century Dictionary  defines bill and coo (by 1768) as "to kiss and caress and talk nonsense, as lovers." Related: Billed; billing.
[written statement] late 14c., "formal document; formal plea or charge (in a court of law); personal letter," from Anglo-French bille, Anglo-Latin billa "a writing, a list, a seal," from Medieval Latin bulla "decree, seal, sealed document," in classical Latin "bubble, boss, stud, amulet for the neck" (hence "seal"); see bull (n.2).
The sense of "written statement detailing articles sold or services rendered by one person to another" is from c. 1400; that of "order addressed to one person to pay another" is from 1570s. The meaning "paper intended to give public notice of something, exhibited in a public place" is from late 15c. The sense of "paper money, bank-note" is from 1660s. The meaning "draft of a proposed statute presented to a legislature" is from 1510s.
[ancient weapon] Old English bill "sword (especially one with a hooked blade), chopping tool," from Proto-Germanic *bili-, a word for cutting or chopping weapons (compare Old Saxon bil "sword," Middle Dutch bile, Dutch bijl, Old High German bihal, German Beil, Old Norse bilda "hatchet"), possibly from PIE root *bheie- "to cut, to strike" (source also of Armenian bir "cudgel," Greek phitos "block of wood," Old Church Slavonic biti "to strike," Old Irish biail "ax").
1580s, "to form a bank or slope or rise," from bank (n.2). The meaning "rise in banks" is by 1870. That of "ascend," as of an incline, is from 1892. In aeronautics, from 1911. Related: Banked; banking.
"to act as a banker," 1727, from bank (n.1). As "to deposit in a bank" from 1833. Figurative sense of "to rely on" (i.e. "to put money on") is from 1884, U.S. colloquial. Related: Banked; banking; bankable.
originally in billiards, "to make (the cue ball) touch the cushion (bank) of the table before touching another ball," by 1909, from a specialized sense of bank (n.2). The verb probably was abstracted from bank-shot (n.), which is attested by 1889. Related: Banked; banking.