I searched up different styles, and I say this style called Gosoku-ryū that has 46 katas including weapon katas. Why would there be katas involving weapons for a style of karate which is an art of the empty-handed?
Just because a karate style may include weapon katas does not mean that the name "karate" is invalidated. You can think of Kobudo as an extension, or sister art(s) to Karate. Okinawan weapon arts are supposed to have been based on farming tools that the practitioners would have had readily available.
Additionally, as has been noted elsewhere, Kara in the original characters for Kara-Te, may not have meant "empty", but rather "China" or "Chinese", referring to the Chinese origin of Karate styles. Take a look at Southern White Crane and compare to Goju-ryu, for example. Probably, the character was changed from Kara ("China") to Kara ("Empty") to remove the art from its Chinese predecessors. Therefore, in its original context, Kara-Te would have no seeming contradiction with weapon arts.
When you practice empty hand way of fighting, that can be karate of which you practice hand to hand fighting. But weapon fighting can also be added of which you learn a fighting system using weapons. On the other hand, those who learn weapon fighting can add in their system empty hand fighting. In the Philippines, the weapon fighting of Arnis is complimented with Arnis de Mano, an empty hand fighting system using the movement of Arnis when manipulating their stick or bolo knife.
'Karate' originally meant 'Chinese Hand'. The change to 'Empty Hand' was essentially a political shift. (The sound is the same, only the writing is different).
The sorting of Martial Arts into distinct fighting styles (striking, grappling, weapons etc) is a relatively modern thing. Historically, people would only have access to one school because of their clan and class. So they covered a much broader range of subjects.
I recommend the Wikipedia entry https://en.wikipedia.org/wiki/Karate
In this era of escalating Japanese militarism, the name was changed from 唐手 ("Chinese hand" or "Tang hand") to 空手 ("empty hand") – both of which are pronounced karate