Daughter to Mr. and Mrs. Peachum and sort-of-wife to Mac the Knife, Polly Peachum is a girl who's caught in the middle. Between her mean old dad and her crazy killer husband, she's got her hands full.
Her dad, Mr. Peachum, calls her a "lump of sensuality" (1.1.178), and her mother is ready to sell her off to the first rich guy who comes calling. Polly herself is pretty naïve, believing Mac when he says, "Today this stable will witness my marriage to Miss Polly Peachum, who has followed me for love in order to share my life with me" (1.2.14-16). Everybody thinks of Polly as something to be bought, sold, or traded. She's a way to increase profits in their eyes.
Polly herself seems to be genuinely well-meaning. When she hears that people were killed when Mac's gang was stealing their wedding supplies, she cries: "Those poor people, all for a few sticks of furniture" (1.2.57-58). But she still marries the guy, which makes her look like weak sauce (in our humble opinion).
But Polly isn't just a spineless little girl. She's got her own, secret ambitions. At her wedding she sings a song about a pirate's bride, Jenny, who is treated badly until she gets her revenge. Polly describes the girl: "[S]he was washing the glasses, and everybody was laughing at her, and then she turned to the guests and said things like the things I'm going to sing to you" (1.2.290-293). And what she sings is pretty chilling.
The song is all about the pirate girl's revenge. When her ship arrives she takes out everyone who has laughed at her: "And they'll ask: which of these should we kill?/ In that noonday heat there'll be a hush round the harbour/ As they ask which has got to die./ And you'll hear me as I softly answer: the lot!/ And as the first head rolls I'll say: hoppla!" (1.2.351-355). So, yeah, she's not exactly meek and mild.
Polly's secret, violent fantasies, are probably only secret and fantasy because she doesn't have much power. If she did, she'd behave like her father and Mac do: killing, stealing, and never thinking twice.