I would assume that what the voice meant by 'strongest weapon' would be your heart, as it is commonly used to represent will power. Strong heart, strong will power. Weak heart, weak will power.
While Riku was, in theory (if you over-analyze the Awakening like I did), supposed to get the KK, he failed to get it because he gave in to darkness. That means in the will power theory that the darkness itself has a will, and it over-powered Riku's to an extent that he gave into the darkness. Sora's rose above it, thus drawing the KK to him. The second Riku's will power was bent, the KK left him.
When Sora goes all emo in the beginning of Hollow Bastion, the KK leaves him because Ansem has basically seized control of Riku, shadowing Riku's will power with his own. And seeing as how Riku was a strong heart before, it would show Ansem had a stronger one at that time than both Sora and Riku. The keyblade would then be drawn to him.
Of course, seeing as how I haven't put KH1 in my PS2 for about 3 years now, this is all based on speculation and possibly weak knowledge. Shows I have to beat it again and refine this.