The manga subverts common tropes:
Yachimidori is not just a passive object of affection; her awkward moments (like the gym class nosebleed or clothing mishaps) are the catalysts for Genki's obsession.
Conclude that the "poor" (kawaisou) in the title applies to everyone involved—Genki for his burden, Yachimidori for her vulnerability, and Sagisawa for her hollow manipulation.