Yes, they ARE illegal in Illinois and most states. They are considered to be a "Slungshot" or heavy weight attached to a line/rope used to do damage to people/things.
For IL statutes 24-1 (Unlawful Use of a Weapon) the blade length is not a factor nor mentioned in the statute. What the UUW statute addresses is "carries or possesses with the intent to use" regardless of blade length.
However, if a person for some reason finds themselves charged with armed violence then the penalty can be increased as an "aggravated offense" if the person is carrying a knife with a blade over 3", along with other named weapons.
(720 ILCS 5/33A‑1)
(1) "Armed with a dangerous weapon". A person is considered armed with a dangerous weapon for purposes of this Article, when he or she carries on or about his or her person or is otherwise armed with a Category I, Category II, or Category III weapon.
(2) A Category I weapon is a handgun, sawed‑off shotgun, sawed‑off rifle, any other firearm small enough to be concealed upon the person, semiautomatic firearm, or machine gun. A Category II weapon is any other rifle, shotgun, spring gun, other firearm, stun gun or taser as defined in paragraph (a) of Section 24‑1 of this Code,knife with a blade of at least 3 inches in length, dagger, dirk, switchblade knife, stiletto, axe, hatchet, or other deadly or dangerous weapon or instrument of like character. As used in this subsection (b) "semiautomatic firearm" means a repeating firearm that utilizes a portion of the energy of a firing cartridge to extract the fired cartridge case and chamber the next round and that requires a separate pull of the trigger to fire each cartridge.
(3) A Category III weapon is a bludgeon, black‑jack, slungshot, sand‑bag, sand‑club, metal knuckles, billy, or other dangerous weapon of like character.