She was advised to play coy, exhorted to come on hearty, exercise, diet, smile and wheedle.
By the third stanza, we're seeing the girlchild a bit more grown up. She's still a young girl, but now she's being told not only what she should look like but also how she should behave.
And how should young girls behave? They should "play coy" (shy) yet also be hearty, exercise (to counter those "thick" legs of course), diet, smile, and use those girlish charms to "wheedle" (coax).
Is anyone else feeling a bit skeeved out? Yeah, us too. And that's probably a good thing for this poem. We're supposed to cringe at all of these ridiculous pearls of wisdom since we understand that this girl is far more talented than anyone gives her credit for.
But instead of embracing her talents, she's told here to curb them entirely and become someone she's not. She should deny her strength by being coy and losing weight and she should smile all the while, even if she's miserable.
So again, we're noticing the speaker's focus here that's revealing the ways adults force young women to fit a mold in order to please everyone else. They're not supposed to please themselves like young men are encouraged to do via sports, academics, leadership, etc. Instead, they need to please others (namely the patriarchy).
Her good nature wore out like a fan belt.
We can kind of see why the girl's good nature would wear out. Her entire experience is wasted trying to be someone she's not.
And the added simile here that compares the wear and tear to a worn out fan belt is right on target.
We notice too that her "good nature" was never quite good to begin with, since it's founded on all sorts of ridiculous expectations coming from everyone else but her. So it's not her "good nature," but rather the nature that society would prefer she has, which kind of contradicts the whole point of "nature."
The added benefit of using the imagery of a fan belt here is that we imagine a running engine, and if that engine can't run properly, it won't run at all. So it's kind of like the whole problem with the girlchild. She can't use her engine (or person) the way it should naturally be used, so she tries to make it run contrary to its purpose, making the whole thing wear out quicker than it should.
So she cut off her nose and her legs and offered them up.
As gruesome as these lines may sound, they're also startlingly indicative of the kind of absurdity the speaker is driving at. If everyone else wants so badly for the girl to look and be someone she's not, might as well get rid of those things all together, no matter if it kills her.
So the point the speaker appears to be making here is that in pressuring the girlchild to be someone she's not. Society is essentially encouraging her to destroy and mutilate herself. If a person can't be who he or she naturally is, then it makes sense that that person can't "be" at all in the eyes of society.
The grotesque imagery we see here also complements the kind of nursery rhyme/fairytale mood that the speaker appears to be working with. Grimm's Fairy Tales are known to be rather dark and gruesome at times, even though they're meant for kids. So we see a similar kind of balance here between childhood sounds and images and their darker connotations that reflect the horrors of the adult world.