The origin of the word Kusari comes from the Kun-yomi reading of the character 鎖, meaning chain.
The word Kusari is probably used because in feudal Japan, Japan had a policy known as "Sakoku" (鎖国), meaning locked or chained country. This policy meant that no japanese could leave Japan and no foreigner could enter Japan, with penalty of death (of course, there were some exceptions). The first character is pronounced "Sa", using the Onyomi pronounciation for the character - an approximation of the chinese pronounciation at the time. Kusari is the original japanese way of pronouncing that character; 'Kusarikoku' would mean pretty much the same. This policy was actually quite famous, I'm sure people here know about it.
The weapon you're thinking of is the kusarigama which is a weapon - pretty much a scythe or sickle on the end of a chain. I'm pretty sure they didn't name it after that though.