The Gaze and the Media

'Men act and women appear' is a popular theme throughout art and entertainment, reflecting an out-dated traditional society. This is also reflected in animation by the overwhelming number of male protagonists compared to female - even male characters seem to outweigh their female counterparts, and generally serve better for story/plot reasons than females, who are there much more as a token, or 'fanservice'.

Jessica Rabbit

The animated film 'Who Framed Roger Rabbit addresses this to a degree. The character of Jessica Rabbit, one of the more main characters is designed in a very exaggerated, overly sexual way. On first glance this looks like it purely serves to entertain the male viewers, the character isn't as 2D as she appears to be, and her most well known quote is 'I'm not bad, I'm just drawn that way'. This not only breaks the fourth way, but particularly points out how it is her design, and the person who designed her who made her that way. Characters who chose to dress or appear one way can be acceptable in moderation as long as it is reasonable, but Jessica Rabbit shows how the female characters serve the whims of their artists, most traditionally male in animation, and appear how males want to see them. This is also another reflection on society - she isn't bad, but society sees her as that from the way she is dressed and appears.

Even other female characters in popular animation are designed with skinny waists, large hips and often large breasts, even when uncalled for or aimed at a young audience. Male characters have a much larger range or designs though, since they are much less expected to conform to certain aspects of society, or at least are accepted more in other shapes because they are male, and therefore have more credibility and abilities than female characters.

Disney, among other companies have been known to change the stories that they are adapting to make their characters much more suitable for romance, or to be seen in a romantic/attractive way. Pocahontas, Snow White and Rapunzel among other characters were all supposed to be much younger in their respective stories, which largely did not focus on romance at all. 

Characters like Rapunzel are increasingly exaggerated to give them a much smaller waist (which carried on to the subsequent film Frozen in which the female characters all looked very similar) and sexualise them. the characters still have fairly childish faces though, which could be seen as an attempt to sexualise or fetishise children. 

Rapunzel

This was probably not intended (at least consciously) and some reasoning given from  Disney executive is that women are 'harder to animate than male ones due to their having to show a "wide range of emotions" and having to "keep them pretty" in the midst of movement". This, understandably, caused a lot of controversy. People come in all sorts of shapes and sizes, and females can make all of the expressions that males can. This shows how even in art and fiction, females are held to these unrealistic standards, when males are given a much larger range of looks and expressions and actions.

Melody, Gravity Falls

There are examples, albeit few of animation treating female characters better and giving them a wider range. In Avatar: the Legend of Korra, the title character Korra is fairly muscular without being portrayed as 'butch' or 'boyish', and is given a very wide range of emotions that don't have to worry about keeping her pretty. Other female characters in the series are designed with different shapes and faces throughout the series are are treated the same as male characters. The same can be said for Gravity Falls, Adventure Time and Steven Universe that portray all kinds of faces and body shapes for their female characters. It could be that animators have more patience/experience when it comes to 2D animation, and an ongoing series is easier to cancel or change than a feature length film, but if so many animations can do it so well, then surely it can't be that hard for 3D to follow in those footsteps and do it too. 3D is still made up of a lot more males though while more females are getting opportunities to work on these 2D animations, showing how it is only the male gaze limiting these characters.