An anecdote began as a story that was not supposed to get out.
The word is Greek anekdota, "things unpublished," built from an-, "not," and ekdidonai, "to publish" or "give out." It was the original title of a sixth-century book by Procopius, a Byzantine scholar who worked as legal adviser and chronicler to Belisarius, the chief general of Emperor Justinian.
In this book he set down court gossip and scandal that he dared not publish while the emperor lived. The Saturday Evening Post's word history says he kept it to himself, fearing retribution, and meant it to appear after his death. In English it is often called the Secret History, or Historia Arcana in Latin, but its original title was Anekdota.
The book then went missing. The Suda, a tenth-century Byzantine encyclopedia, mentioned it. The text itself was lost for a long time and, the Post says, turned up in the Vatican Library in the 17th century and was printed. That article does not give a more specific year for the printing.
The word reached English either through French anecdote or directly from Medieval Latin anecdota, according to Etymonline, which dates English use to the 1670s with the meaning "secret or private stories." That is still close to the title of Procopius's book.
The meaning then drifted. Etymonline records "brief, amusing story" by 1761. The Post says that by the 18th century the word commonly meant a short, entertaining story about a person, not a story offered as proof of something.
That later sense is why "anecdotal evidence" now sounds weak. A single personal story is an anecdote, and the word has lost its link to secrets.
The family grew in a few steps. Etymonline lists anecdotical from 1744, anecdotal from 1794, and anecdotage from 1823, a joke word that by 1835 meant garrulous old age.