I think most martial art systems have a striking, grappling, and weapon component. The older the system the more likly all three would be a part of the system.
This is true of many CMA. For karate, it depends on the era you're talking about. From the beginning, having evolved from CMA, Okinawan karate had striking and grappling (mostly grabbing and twisting, take downs, but a few throws too). For some reason, the Okinawans who studied in China (while they may have learned Chinese weapons) did not appear to teach them.) Let's call this time period 1800's.
Now, many karate experts in this time period knew weapons - kobudo, tools of the warrior - Samurai sword, staff, sai and spear mostly, but I have not seen where they were part of the karate curriculum. It seems that they were a separate, parallel, area of study, independent of the karate system. Some non-karate people like farmers practiced weapons such as eku (row boat oar), staff, nunchaku and tonfa (all simple wooden implements) and kama (sickle) for self-protection, though to what extent I don't know.
By 1900, a new era emerged. Okinawa was now firmly under Japanese control and law enforcement. Traditional weapons were really not needed too much by anyone on the Ryukyu islands, so their usage (and knowledge of) declined. Noting this atrophy of Okinawan weaponry, Taira Shinken began to accumulate the techniques and kata of both the warrior and peasant class (sometimes disguised as folk dances).
A contemporary and student of several karate masters in the first half of the 20th century, Taira shared his knowledge with them, or learned from them. In this way, karate got the last part of the triad you referred to. So by 1950, kobudo became entwined as part of many Okinawan karate styles and the tradition was preserved and passed on. (The Samurai sword remained a separate study, being essentially a Japanese art.) Some dojos do not teach any weapons.
Kobudo also still exists as a separate discipline, outside of Karate, and there are about 3 main styles specializing in traditional weapons. Some esoteric weapons may be taught there that karate dojo don't get into. A number of karate practitioners also study in one of these specialized styles, wanting to delve further into weapons than karate dojo offer.