This came up over my family vacation this past week: I was talking with my sister and she, being frustrated at some local government red tape, referred to it as "Byzantine." I responded that that was a racist term and they preferred to call themselves Rhomaioi, not Byzantines. So when and why did the term pick up such negative connotations instead of just referring to the great, 1000-year empire of the Eastern Romans? I would assume it was after the particular historian decided to start referring to the empire centered on Constantinople/old-Byzantion, as the Byzantine Empire.
Thanks for your time in reading this and maybe responding. I've been a long-time reader of this subreddit but I think this might be my first actual posting of a question.
Quite recently, accordingly to the Oxford English Dictionary (OED).
"Byzantine" in the sense of "pertaining to Byzantium" is of course an old word; but the earliest verified use for the Empire, in English, is from 1693 (C. Blount, Oracles of Reason: “The Goths, who at that time possessed of Italy, Spain, Afric and other Provinces, were formidable to the Bizantine Empire.”). In Latin it's older; we see Imperium Byzantinum or Byzantinum Imperium at least as early as 1596 (Leorino, Selectissimarum orationum…: …virumque imperium Byzantinum & Trapezuntinum in Græcia…); and probably a few decades earlier, if we can trust Google Books.
But the earliest OED verified mention for the derogative meaning is as late as 1937, from Koestler’s A Spanish Test: "In the old days people often smiled at the Byzantine structure of the Spanish Army." I found no older English uses of this sense on Google, either. Before the 30s it was in widespread use to describe the art, architecture and styles of Byzantium; the derogative meaning may be a semantic shift from the artistic one (compare the adjective "baroque").