So the sky's the limit. The Japanese keep this ethic of limitless creativity in mind when creating their animated features. All in all, Western animation may mostly be for kids, but Japanese animation has a much wider scope. The reason for this is as old as cartoon animation itself, and the cause, or maybe blame, can fall upon Disney and his proteges. One of three reasons this is still done, apart from the trademark style, is the need for emotional expression.
Bigger eyes allow for better emotional reactions in the characters faces.
Finally, the last reason for big eyes is the most evasive. Unless you're Japanese, then you might not know the cultural significance behind eye size. In tradtional Japanese culture, a person with small eyes may be considered dishonest, evil or just plain shifty. This is almost begging the question of their nasty intentions. Both formats have their advantages and disadvantages.