Sorry about that, the old app format I'm used to tend to dock points for counting too much on other characters in the work, or going too far into headcanon, I'll be glad to elaborate! Also spoiler warnings for all of the show:
A lot of what Hamilton does and says seems to come from personal tragedy and how he deals with it. Like one of the best ways I've seen it explained is when Lin Manuel Miranda said that "There's a crack in the foundation, really early in his life". He'd seen his father abandon him and his mother, he was sick with fever when his mother died right beside him and he lost nearly everything that his mom owned. Shortly after that the cousin who took him in committed suicide, and he lived through a hurricane which claimed over two hundred people. Go even further down the line and he sees the horrors of the revolutionary war and in particular, Valley Forge. He loses Laurens shortly after the birth of his son, and nearly two decades later, he loses his son as well. His life is a series of constant hardships that he's always recovering from, even before his mouth gets him in trouble.
The thing is that many of these horrible things mostly get a passing mention at best, and I like to think that matches how Hamilton tries (or more accurately, tries not to) deal with those events. Like there's two songs that directly talk about these things, and then the rest is like "oh yeah btw this happened". Hamilton for the most part says what he thinks and feels, yet he never really tries to work through all those old wounds himself. Instead it comes out as endless hard work to keep his mind busy, or a quick temper, or even simply bottling it up and saying that it's "unimportant". He doesn't want to deal with it until he breaks, and eventually? He does break. Phillips' death cripples him in a lot of ways, and even after he becomes more politically active again, it's not at the same breakneck speed.
This isn't the only factor though, there's also the fact that his social and financial background means that he'd be pretty dismissible to the generally well-off intellectuals in college and after the war. He has to fight everyone, he has to work twice as hard, he has to make choices that aren't popular, and he has to think about his legacy. Because even if people hate him for it, at least he left a mark and he won't be forgotten.
On Burr: Oh boy, Burr is complicated. In many ways Burr is the counterweight to... everything Hamilton does, and Hamilton knows that. It's frustrating for Hamilton, but he also realizes that sometimes you do need to hold back for just a moment or compromise, and he acknowledges that the guy can sum up an argument persuasively and in fewer words than Hamilton does. However that doesn't mean he's happy with the idea, and for the most part he doesn't like how Burr seems unwilling to pick a side.
On a personal level he has mixed feelings in so many ways. On one side this is the man who he's worked with and thought of as a friend for many years. However on the other this is also the same guy that switched political parties and got Eliza's father out of office, just for a senator seat. In fact that was the exact moment something went wrong in their friendship, while Burr said that he didn't understand why they couldn't still be friends, he didn't pick out the note of open betrayal in Hamiltons' voice. After that the list of disagreements kept piling up, from Burr being in the group that went after his financials to try and remove him from power, to- yanno, killing him. They have so much bad blood between them that Hamilton even sides with Jefferson over Burr, which is a shame because the same components of what made them friends still lie under the surface. At the end of the show it's clear that Hamilton has deeply conflicting feelings about Burr, if he was an actual enemy and truly dangerous he would've shot him, but he didn't. Instead he recognizes him as someone that once was a friend, and raises his pistol to the sky.
On Eliza: Oh Eliza, she really, really is too good for this man, and he's acutely aware that he's been given far more chances than he deserves with her. Frankly, he adores Eliza, and not only for her kindness. He loves her mind, the steel of her spine, her grace, and when he calls her the best of wives and women he means it. She can't keep him from doing something he's set his mind to, but he still does listen to her, confides in her, and she's an incredibly positive force in his life. He also feels incredible guilt towards her. Not only did he cheat on her for months, but he advised Phillip about what to do during the duel, he gave Phillip his pistol. If Phillip had gone to Eliza, he might've survived. Even if his feelings of guilt hadn't been firmly set in stone yet, Eliza's half-wailed, nearly screamed "Who did this, Alexander, did you know?" would've crystalized them into something he could never forgive himself for. To him, it's a miracle that she eventually forgave him, much less that they repaired their relationship.
Re: Revision
A lot of what Hamilton does and says seems to come from personal tragedy and how he deals with it. Like one of the best ways I've seen it explained is when Lin Manuel Miranda said that "There's a crack in the foundation, really early in his life". He'd seen his father abandon him and his mother, he was sick with fever when his mother died right beside him and he lost nearly everything that his mom owned. Shortly after that the cousin who took him in committed suicide, and he lived through a hurricane which claimed over two hundred people. Go even further down the line and he sees the horrors of the revolutionary war and in particular, Valley Forge. He loses Laurens shortly after the birth of his son, and nearly two decades later, he loses his son as well. His life is a series of constant hardships that he's always recovering from, even before his mouth gets him in trouble.
The thing is that many of these horrible things mostly get a passing mention at best, and I like to think that matches how Hamilton tries (or more accurately, tries not to) deal with those events. Like there's two songs that directly talk about these things, and then the rest is like "oh yeah btw this happened". Hamilton for the most part says what he thinks and feels, yet he never really tries to work through all those old wounds himself. Instead it comes out as endless hard work to keep his mind busy, or a quick temper, or even simply bottling it up and saying that it's "unimportant". He doesn't want to deal with it until he breaks, and eventually? He does break. Phillips' death cripples him in a lot of ways, and even after he becomes more politically active again, it's not at the same breakneck speed.
This isn't the only factor though, there's also the fact that his social and financial background means that he'd be pretty dismissible to the generally well-off intellectuals in college and after the war. He has to fight everyone, he has to work twice as hard, he has to make choices that aren't popular, and he has to think about his legacy. Because even if people hate him for it, at least he left a mark and he won't be forgotten.
On Burr: Oh boy, Burr is complicated.
In many ways Burr is the counterweight to... everything Hamilton does, and Hamilton knows that. It's frustrating for Hamilton, but he also realizes that sometimes you do need to hold back for just a moment or compromise, and he acknowledges that the guy can sum up an argument persuasively and in fewer words than Hamilton does. However that doesn't mean he's happy with the idea, and for the most part he doesn't like how Burr seems unwilling to pick a side.
On a personal level he has mixed feelings in so many ways. On one side this is the man who he's worked with and thought of as a friend for many years. However on the other this is also the same guy that switched political parties and got Eliza's father out of office, just for a senator seat. In fact that was the exact moment something went wrong in their friendship, while Burr said that he didn't understand why they couldn't still be friends, he didn't pick out the note of open betrayal in Hamiltons' voice. After that the list of disagreements kept piling up, from Burr being in the group that went after his financials to try and remove him from power, to- yanno, killing him. They have so much bad blood between them that Hamilton even sides with Jefferson over Burr, which is a shame because the same components of what made them friends still lie under the surface. At the end of the show it's clear that Hamilton has deeply conflicting feelings about Burr, if he was an actual enemy and truly dangerous he would've shot him, but he didn't. Instead he recognizes him as someone that once was a friend, and raises his pistol to the sky.
On Eliza: Oh Eliza, she really, really is too good for this man, and he's acutely aware that he's been given far more chances than he deserves with her. Frankly, he adores Eliza, and not only for her kindness. He loves her mind, the steel of her spine, her grace, and when he calls her the best of wives and women he means it. She can't keep him from doing something he's set his mind to, but he still does listen to her, confides in her, and she's an incredibly positive force in his life. He also feels incredible guilt towards her. Not only did he cheat on her for months, but he advised Phillip about what to do during the duel, he gave Phillip his pistol. If Phillip had gone to Eliza, he might've survived. Even if his feelings of guilt hadn't been firmly set in stone yet, Eliza's half-wailed, nearly screamed "Who did this, Alexander, did you know?" would've crystalized them into something he could never forgive himself for. To him, it's a miracle that she eventually forgave him, much less that they repaired their relationship.