When I first came to Japan over a decade ago(oh, my god!), one of the first things that confused me and I thought was funny was seeing adult Japanese women making this silly pouty face. I couldn't understand it. They'd scowl and puff out their little cheeks like chipmunks. Where they joking? In the west, only little kids act like that. Well, now I know better. It may look childish to us, but watch out guys. If your Japanese girlfriend shows you this face, it means she is genuinely angry with you and should be taken seriously. The Japanese are not usually overly emotional in public and this face is a socially acceptable way for women to show their anger without looking too angry. And anyway, it is kind of cute.
I can't take credit for these photos. I found them online because I couldn't get anyone to model for me. By the way, you never see Japanese men puff out their cheeks like this, at least not if their straight.