saying n.

Middle English seien, from Old English secgan "to utter, inform, speak, tell, relate," from Proto-Germanic *sagjanan "to say" (source also of Old Saxon seggian, Old Norse segja, Danish sige, Old Frisian sedsa, Middle Dutch segghen, Dutch zeggen, Old High German sagen, German sagen "to say").

Watkins has this from a PIE *sokwyo-, from a root *sekw- (3) "to say, utter" (source also of Hittite shakiya- "to declare," Lithuanian sakyti "to say," Old Church Slavonic sociti "to vindicate, show," Old Irish insce "speech," Old Latin inseque "to tell say"). Some further see this as identical to the PIE root *sekw- (1) "to follow" (with semantic development to "see" and then "speak"). But others doubt it and Boutkan gives it "No certain PIE etymology."

The past tense form said developed from Old English segde. Impersonal use (it is said) was in Old English. The notion in shall we say, etc. (1580s) is "suppose, take for granted." On that analogy, impersonal say is used as an introduction word, or parenthetically, with a clause and meaning "suppose, assume" (c. 1600). Its colloquial use as an expression of surprise, etc. is by 1830.

Not attested before 1930 in use with inanimate objects (clocks, signs, etc.) as subjects. You said it! "you're right" is attested by 1919; you can say that again as a phrase expressing agreement is by 1925, American English colloquial. You don't say(so) as an expression of astonishment (often ironic) is attested by 1779. The Society of American Florists' advertising slogan say it with flowers dates to 1918 from it grew other say it with constructions.

1520s, "concise statement of a principle" (especially in reference to the "Aphorisms of Hippocrates"), from French aphorisme (corrected from Old French aufforisme, 14c.), from Late Latin aphorismus, from Greek aphorismos "definition; short, pithy sentence," from aphorizein "to mark off, divide," from apo "from" (see apo-) + horizein "to bound" (see horizon).

The general sense of "short, pithy statement containing a truth of general import" (e.g. "life is short, and art is long") is from 1580s in English. Distinguished from an axiom, which is a statement of self-evident truth; an epigram is like an aphorism, but lacking in general import. Maxim and saying can be used as synonyms for aphorism, but maxims tend to be practical than aphorisms, and sayings tend to be more commonplace and have an author's name attached.

[F]or aphorisms, except they should be ridiculous, cannot be made but of the pith and heart of sciences ; for discourse of illustration is cut off ; recitals of examples are cut off ; discourse of connexion and order is cut off ; descriptions of practice are cut off. So there remaineth nothing to fill the aphorisms but some good quantity of observation : and therefore no man can suffice, nor in reason will attempt, to write aphorisms, but he that is sound and grounded. [Francis Bacon, "The Advancement of Learning," 1605]