Because even if what the child does is insignificant, even if it is just casual behavior, the mother thinks that the child has come specially for her, which makes her feel very satisfied.
Maybe this is the only evidence she can get from me. In the sentence, "evidence" means (the author gave his mother a sweet card when he was fourteen). I will just ... keep asking her for more evidence. In the sentence, "evidence" means (proving that my mother loves me).