All the Mikeys of all the timelines, even those who still don't know him as little Mikey or the one from the original universe, cried, I think that if canon Mikey saw all the times that Takemichi has risked his life, died, see his friends die and not being able to do anything, being betrayed by himself and still going ahead to save him, he would realize how important his happiness is to him.
Maybe he realized how much Takemichi cares about him and cried because he remembered his other friend, Draken, and the only one who cares about him and who is still alive will die by his side.
I’m still sus of MiTake, ! MANGA SPOILER ! they might be siblings. Mikeys dad looks awfully a lot like Takemichi and Shinishiro is the second time leaper so it might run in the family… also, take and shin look a lot alike too according to mikey, baji etc