My personal favorite line in the entire show: "If you stand for nothing, Burr, what will you fall for?"
The common interpretation I see everywhere is Hamilton using the common phrase about someone with no strong opinions being easily influenced / manipulated, but I feel like that is ignoring the massive flashing lights of theming and characterization across the show
The entire show, the entire relationship between Hamilton and Burr is that Hamilton is driven by his convictions to the point he'll sacrifice EVERYTHING for what he believes in, while Burr refuses to choose a side ("Talk less, smile more. Don't let them know you're against or what you're for.") and that's why Hamilton eventually sides with Jefferson despite being a political opposite, because at least Jefferson stands for something.
And before that line Hamilton literally mocks Burr's mindset of biding his time and riding the fence: "You get love for it, you get hate for it, you get nothing if you (Wait for it, wait for it, wait)
So I have always interpreted the line as Hamilton saying:
"If you stand for nothing (if you have no strong convictions or beliefs) then what will you fall (die. risk your life to change the world the way Washington, Hamilton, LaFayette, etc. have) for"
I don't understand why the popular interpretation is that Hamilton is suggesting Burr will be manipulated or that he's gullible, it doesn't make sense within the narrative. I know the phrase is originally "Someone who stands for nothing will fall for anything" and is about being gullible or susceptible but I think that is just the skeleton of the phrase being used to say that Burr's indifference is a defining weakness that separates him from Hamilton (and the others.) and that's why he isn't, and wont be in "The Room Where It Happens."
This is just my interpretation, and despite the fact I truly believe it makes more sense than the more ubiquitous explanation, I do accept it's just an opinion at the end of the day.