In Hamilton: The Revolution, it it said how Eliza was a difficult character to write. She was just so generically good, but to have an interesting story, you need to have a character who's more than that. You need struggles and flaws for them to overcome! Not much of Eliza's history comes from her, instead from friends and acquaintances that wrote about her. They said she was a charming, loving and dedicated person, and it certainly shows in the musical.
The first time Eliza makes an apperance is in The Schuyler Sisters. In the song, you learn that they are part of a rich family, and are introduced as strong, independent women, excited to see what the revolution will bring. Eliza sings: Look around, look around, at how lucky we are to be alive right now!
Next is Helpless, in which Eliza meets Alexander Hamilton. They fall in love and get married and all that good stuff. Alexander tells her how he's poor, but she really doesn't care.
The next song Eliza plays a big part of is That Would Be Enough, when Alexander returns home from the war temporarily and finds out that Eliza is pregnant with their first child. Eliza tries to convince Alexander not to go back to the war: Oh, let me be a part of the narrative, if the story they will write someday. Let this moment be the first chapter, where you decide to stay...
In act II, a bunch of other stuff happened, and I don't want to spoil it all, but one thing that happened is that Alexander commits dum-dum and cheats on Eliza. In the song Burn, she sings about her side of the story. She burns Alexander's letters to her: I'm erasing myself from the narrative. Let future historians wonder how Eliza reacted when you broke her heart. You have torn it all apart...
It's Quiet Uptown takes place after their son Phillip's death. It's about their grief over losing him, but it's also when she decides to forgive her husband. I think Eliza's compassion really shows here, even if Alexander probably doesn't deserve it.
The last song of Hamilton, titled Who lives, Who Dies, Who Tells Your Story tells how Eliza worked to tell the stories of Hamilton and like half the other people in the musical. She put herself back in the narrative. They ask: And when you're gone, who remembers your name, who keeps your fame, who tells your story... And the answer is Eliza.