The Bavarian Illuminati is the rare secret society whose internal documents were captured intact. When the Elector banned secret associations and the order was suppressed, Bavarian officials raided the houses of members, seized the correspondence, and published a selection of it in the late 1780s specifically to discredit the movement. The result is that historians can read what the order actually wrote to itself.
What the papers show is a graded recruitment system, running from Novice and Minerval upward, in which members were watched and assessed before being told anything, and in which Weishaupt spent a great deal of energy on internal politics. The programme was Enlightenment reform: reduce the influence of the church and the nobility over education and public office, by placing sympathetic men in posts. Membership peaked at a scale of hundreds to low thousands, over roughly a decade.
The afterlife dwarfs the thing itself. In 1797 and 1798 the Abbe Barruel in France and John Robison in Scotland published books arguing that the French Revolution had been engineered by the Illuminati working through Masonic lodges. Neither had evidence for it. Both were widely read, and every subsequent conspiracy literature about a hidden hand behind world events descends from them. The order had been dead for ten years when the story about it began.