可愛がる
かわいがる · kawaigaru · JLPT N2 · verb-godan
to be affectionate
🐶 可愛い (cute) + がる (to treat as) = treat as cute, i.e. to dote on and love
がる is a verb suffix meaning to treat something as or show signs of a feeling, as in 欲しがる (to want). So 可愛がる means to treat someone as cute, which is to be affectionate toward them.
可 — mouth 口 + breath marker 丁 (modified)
可 originally depicted a mouth (口) with a curved stroke suggesting exhaled breath or speech, conveying approval or assent. From this came the meaning 'to permit' or 'can,' as granting permission was expressed verbally. Today it broadly means 'may,' 'can,' or 'approve.'