A collection of thoughts I have had in my many times listening to Hamilton.

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The piano parts in Satisfied and Burn are really similar, Satisfied just being slightly faster and having a couple extra notes. Both also end with a guitar strum that ends with a bit of discord. In That Would Be Enough and It's Quiet Uptown the strum is also present, although in It's Quiet Uptown, the discord is mostly gone. The reasoning behind this (I think) is how in all the other songs, there is some kind of conflict. In Satisfied, Angelica can't have Alexander. In Burn, Hamilton cheated on Eliza and she is burning his love letters, and in That Would Be Enough, Eliza is trying to convince Alex to stay and be content with her and their child. However, in It's Quiet Uptown, their conflicts are resolved.

The melody when Phillip and Eliza count to 10 in French is the same was when they count to ten in Ten Duel Commandments, foreshadowing of Phillip's duel.

Phillip always changed the melody while counting with his mother at the number 7. He was fatally shot in his duel with Eacker on 7, and in Stay Alive  Reprise his heart stops beating and he dies on 7.

Burr's phrase throughout the musical is "wait," whereas Hamilton often says "just you wait." Burr is waiting, while Hamilton wants everyone else to wait.

There is a steady beat going on whenever someone dies; is is happening in Stay Alive Reprise and stops when Phillip dies; happens again in World Was Wide Enough and stops when Burr says the line "Angelica and Eliza... were both at his side when he died." and stops right on ‘were,’ so probably when Hamilton died. It probably represents the heartbeat.