I once took a Psychology course which had another explanation for the large eyes. Apparently, when humans are sexually aroused, their pupils get larger. This makes people with larger pupils more sexually appealing, leading to all kinds of tricks to making your pupils larger (for example, candlelit dinners; also, in some older civilizations, women used to use eyedrops to make their pupils larger).
All of this leads to people thinking larger pupils look better, and in the case of small cartoon characters, look cuter.
"It has a long history of use as a medicine, cosmetic, and poison. Before the Middle Ages, it was used as an anesthetic for surgery, the ancient Romans used it as a poison (the wife of Emperor Augustus and the wife of Claudius both used it to murder contemporaries) and predating this it was used to make poison tipped arrows."
and
"Drops prepared from the belladonna plant were used to dilate women's pupils, an effect considered attractive."
All of this leads to people thinking larger pupils look better, and in the case of small cartoon characters, look cuter.