Because some people like women with big breasts. As usual, anime exaggerates; it can't just have a woman with big breasts, it has to have a woman with ridiculously gigantic breasts.
This isn't purely a Japanese thing. Actually, I would argue that it came in origin from American media that were exported to Japan. In the US, large breasts are often considered more attractive. The supposed ideal of American young men's fantasies is 36D-24-36: 36 inches around the chest, cup size D, 24 inches around the waist, 36 inches around the hips (the "hourglass" shape). There are even articles using these three-sizes as a shorthand for the tyranny of societal beauty standards.
The epitome of this standard of beauty in American media is Jessica Rabbit from Who Framed Roger Rabbit?
Women with large breasts are also common in American comics:
Anime and American comics both tend to exaggerate everything, so essentially they took a preference for large breasts and massively exaggerated it, to the point that characters have J-cup breasts. (US readers, keep in mind a Japanese J cup is an American H cup.)
Japan gets a ton of American media, so there have been ample opportunities for this American love of big boobs to seep into their culture. My theory is that it started during the US occupation with pinup posters brought over by the servicemen:
Then it was refreshed with every Hollywood movie that came in showing men lusting after women with big breasts.
Speaking of Jessica Rabbit, Cracked has an interesting theory on psychological and evolutionary reasons why animated women with ridiculously exaggerated boobs appeal to viewers. They're obviously a humor website and not a peer-reviewed scientific journal, so take it with a grain of salt.