What I meant was that the dots, or the points, or whatever you want to call them, are the points of the object's DEATH. It is the LINES where the life force is the weakest, which makes sense since they do connect the points of death. So Shiki basically destroys the object's form when tracing the lines, and kills it when stabbing the dots. They are similar in nature, just the opposite in order. By tracing lines, Shiki destroys the form which in turn kills the object. When he stabs the dot, Shiki kills it, which results in the destruction of its form.
Also, the dots that Shiki sees are the points of the object's death, not its weakest point. Once stabbed, that is it. The dots doesn't cause the greatest damage to the object. It INVOKES death, which is what makes Shiki's eyes so impressive. This is the official setting of Tsukihime. I am not making this up.
As for as Shiki in Kara no Kyoukai, or the girl Shiki as I will refer from here on, Tsukihime Shiki and the girl Shiki basically sees the same thing, just by different methods. Tsukihime Shiki already had a special set of eyes passed down on his Nanaya family, which can see things that cannot be seen, and when he experienced death, the eyes evolved into what they are now. In case of the girl Shiki, she was connected to the Origin of All Things since birth(why and how were not explicitly explained in the novel, except that she is born with it.). So she understands and sees the death on everything, including abstract things, at a much less cost than Tsukihime Shiki.
The reason the girl Shiki can see death of things that Tsukihime Shiki cannot is the difference in capacity. Although Tsukihime Shiki has special eyes, he still has to use his own brain to process the death of an object. So Tsukihime Shiki cannot see death on things that he himself cannot understand the concept of its death. The girl Shiki is different. She can basically understand anything's death by just accessing her connection to the Origin. Her brain does not have to understand because she is already connected to the gigantic supercomputer called the Origin. So she can see death on things even though herself does not really understand it