So in the last minutes of the episode 16 Kaori (while in bed) tells the next thing to Kousei:
I know for the dubs it can be a little bit off and the real meaning can change, so i read more about it and the meaning can also change from "double" to "lovers"; "lovers suicide" in the Japanese culture is used to describe the practice of lovers to suicide (da) when they couldn’t get to be together and marry for social/familiar reasons.
I am not sure if I am doing right by bringing this now, but I can’t let go the anime, even I don’t know why I am holding this hard to it.
So I have a theory here and this is going to sound harsh and maybe cruel, but Was a declaration of love to Kousei. And the more I think about the more it makes sense (or so i want it to make): the not "fitting" into Kouseis Group of friends(social circle), Kaori didn’t wanted to destroy the relationships between Kousei and Tsubaki as she knew she was not going to be around for much time, and by saying it directly to Kousei she loved him, at the end she would had only teared apart his heart (driving him into a bigger grudge) so by saying to commit suicide with her I think she was saying: "I love you, but your heart will die when I die"(ending his life as well, o so I believe). I know they where 15 years old, but who knows, maybe Kousei got the memo and understood, explaining why he doesn’t cry when reading the letter.
Tell me what you think. And thank you for reading. XD here take a potato.