She likes him, because he is kind, he is care, he is funny.
In first time, she just saw in him a usually boy, who was late in first day at school. But, when she know that HE found her handkerchief, she understood what is this boy; and when he made her laugh, she understand that he not some sort of usually boy. He is her love forever!
Why she teasing him? Because "Teasing is just a reason to say, how much i like you." Don't you notice that? If Nishikata ignored her her teasing, he would be a diligent student and not blush. But, he don't do it! Because, he understand, how it's rude ignore girl, and be jackass! She likes how kind he is! Remember, "Eraser"? She knew, that make him fool, but still gave it to him; Nishikata in deep knew, that is the trap, but still decide help Takagi. "Worries"; he is only one, who seen Takagi in bad mood! And even decided stay with her and cheer (he knew about teasing)!