The fact that Eliza forgave for Alexander means so, so much.
He cheated on her, broke her trust, and still continued to think only about himself - ”[Teling everyone that he cheated on his wife] was an act of political sacrifice.”- Congratulations. - and yet, she forgives him.
They were both grieving, both could have reacted differently, and she forgives him. I believe it was some form of a coping method. Forgiving Alexander would make everything easier; they wouldn’t have to argue and they could learn to deal with everything together.
What I’m trying to say is: Eliza is a saint. If I were here, I would walk away from him and learn to cope with my sister, but she forgives him, lets him off for everything he had done.
She goes on to do so much more for him, even though he treated her awfully.
”I interview every soldier who fought by your side.” - She tries to get to know the other, war-version, side of Alex.
“I try to make sense if your thousands of pages of writing.” - She tries to understand his trail of thought. She wants to understand him. She loved him with all her heart. She still after he cheated; she still did after he treated her awfully; she still did after his death.
“I raise funds in D.C. for the Washington Monument.” - Washington felt like a father to Hamilton, even though the line “I’m not your son!” exists. You can not deny that they weren’t close. They were, and Eliza raises funds for him because of this.
“I speak out against slavery.” - This was something Alexander, and his
other lover best friend, believed in strongly. This was something she believed in strongly. She fought against it for herself, for Alexander, for everyone’s freedom. She didn’t do all of this for Alexander; she did still have her own morals. She just tried to do the right thing, and that's one of the many reasons I love her.
“I established the first private orphanage in New York City.” - Alexander was an orphan, and she, obviously, knew that. She established this to help the kids, to stop children from having to deal with what Alexander went through. She knew how awful it was, she saw it in her husband, and she tries to help them through it.
She helps so many (”I help raise hundreds of children.”) and the main, probably reason, was for Alexander’s legacy, something he always wanted.