The story is simple, but kinda complicated too:
When Weiss is given a mission by Persia, their leader, they must execute it using their special abilities and their cool weapons. Aya uses his slick samurai sword. Just his type... the kind of silent justice. Ken wipes out his victims with razor-sharp tiger claws. Omi uses the distance to his advantage by shooting his enemies with a different kinds of darts and arrows. Omi is also the smarts behind Weiss. He uses his computer skills to hack into computers and gather information their mission. Youji strangles his targets with an almost-invisible wire, leaving hanged corpses. (I call it floss for very rough teeth.)
Weiss disguises themselves as four florists working at the "Kitty in the House" flower shop. Most of the girls from the local high school come to visit them, buying flowers and plants just to get a glimpse or a 'Hi' out of them. Youji, the ladies man, likes the attention as the ladies swarm around him, but he says that he leaves all the girls under 18 to Omi and Ken. Omi and Ken are quite amused by the girls' adorations of them, but Aya is the most uncomfortable of the group of girls.
Persia gives Weiss their mission to assassinate the Takatori crime boss, Takatori Reiji. In order to do this, Weiss must eliminate Takatori's cronies. In the first few episodes, you learn more about the pasts and experiences that Aya, Ken, Youji and Omi have gone through that has involved them with Weiss. The first mission involves Weiss discovering a group of four rogue assassins who are out to find a certain disk to access important documents for Takatori. The second mission Aya finds out that Takatori Reiji was the one responsible for putting his younger sister into a deep coma after a hit-and-run. The second mission succeeds, yet also fails because Aya cannot exact his revenge on Takatori. The third mission centers on Youji as he runs into a cute woman who resembles his old partner when Youji was a private investigator. Youji must face his past in order to deal with the present situation he is facing and also completes his mission. In the fourth mission Ken finds his old friend Kase Kouichiro, who was kidnapped by Takatori a long time ago. Ken finds out that his friend is not really the true loving friend that he thought he knew.

Well your probably asking 'Why does Aya have a girls name?' Well the answer is that Aya is his sisters name. He took it ever since she was in coma. He wanted to live her life for her and in the meantime get revenge for who did that to her. Aya's real name is Ran. In the subtitled version of Weiss Kruez, they distinguish them buy adding a 'kun' and a 'chan'.