But that's not important. I just thought it would be fun if someone could explain the history of these things and give context as to how they became a part of Southeast Asian martial arts in the first place. Or were they in other parts of the world as well?
Nunchaku became a well-known martial arts weapon through Bruce Lee (e.g., his use of them in Enter the Dragon), and then a whole bunch of stuff adopting them, probably from their use by Bruce Lee (more ninja movies than you want to shake a stick at (hinged or otherwise), Teenage Mutant Ninja Turtles, and more). As a result, they're much more widely used than the original martial art they were used in (they're one of the old Okinawan karate weapons), and are also used in karate much more often today than before all that pro-nunchaku publicity.
The main Okinawan karate weapons are police weapons, and they probably dominate Okinawan karate weapons because Okinawan karate largely descends from Okinawan police martial arts (from the 15th century through to the 19th). It is often said that Okinawan karate comes from the peasantry, and the weapons are peasant farming tools adapted to weapons in order to fight the Japanese occupiers, and that the nunchaku was originally an agricultural flail. However,
The ancestry of karate is much more likely to be police martial arts [1,2], which in turn have roots in Chinese martial arts.
The nunchaku much more closely resembles Chinese fighting flails than agricultural flails. For an example of a Chinese civilian fighting flail, possibly for police use, see http://mandarinmansion.com/chinese-fighting-flail and figure 284 in Stone's Glossary [3] (while on these flails, the handle is longer than the head, equal-length flails were used in China). Military flails typically have metal spikes or solid metal striking heads, while on this flail, the only metal part is the hinge.
Other Okinawan karate weapons such as the sai and bo were used for police purposes in China. (The sai was also used in Indonesia and continental SE Asia.)
While it isn't the only possibility, the best explanation appears to me to be that the nunchaku is the Okinawan version of a Chinese police weapon (ditto, the sai), a police truncheon-flail.
Flails were used in many parts of the world, and I gave some examples in my answer to https://www.reddit.com/r/AskHistorians/comments/9i66ht/did_the_chain_morning_starflail_weapon_actually/ but nunchaku as such - short, light, wood except for the hinge, equal-length handle and head flails - are much less common, and the only pre-modern examples I know of are Chinese and Okinawan. (Other flexible weapons were used for police work, such as the manrikigusari in Japan.)
Nunchaku see some use in modern police forces, sometimes as a striking weapon (i.e., a truncheon-flail), and sometimes purely as a restraining tool (clamp the two halves over, e.g., the target's hand, and squeeze).
Finally, not all of the traditional karate weapons are police weapons. Sword and shield, and spear were originally military weapons, and the oar (eku) is a rather fearsome club.
References:
[1] Kevin S. Y. Tan, "Constructing a martial tradition: Rethinking a popular history of karate-dou", Journal of Sport and Social Issues 28(2), 169-192 (2004).
[2] Patrick McCarthy, Bubishi: The Classic Manual of Combat, Tuttle, 2016.
[3] George Cameron Stone, A Glossary of the Construction, Decoration and Use of Arms and Armor: in All Countries and in All Times, Southworth Press, 1934. (Available in various modern reprints, including Dover.)