After rewatching/reading this scene a couple times, I've come up with a speculative explanation about what Happy Chaos is saying in this scene:
"Scales... A well-calibrated scale uses counterweights to keep itself from breaking. Order, systems, stability. A scale that doesn't move is no scale at all."
The first two lines are self-explanatory, while the third line listed possible examples of counterweights for whatever the scale was meant to represent. Though the words used were still quite broad to fully guess what it could mean, since maintaining anything helps prevent it from breaking. That is, it must remain stable, often through order, that is created by systems. And whatever the scale is meant to represent, it is something that loses purpose or meaning the moment it is not used.
"That's not allowed."
And we either don't want that, or it's something that shouldn't happen for some reason. That reason being:
"The world as we see it is shaped by mankind's emotions."
So, here's my theory: scales. Whatever the scales are meant to represent, they are nonetheless used for balance. And the world is still unbalanced, because mankind allowed emotions to run rampant. We have known that in the Guilty Gear universe, too much emotions already caused problems in the past, as Jack-O explained:
"...the world got possessed by humanity's emotions during the war. So the backyard cut off the source of the illness. That was the first mistake. The part that got cut off was given tremendous authority. And became all-powerful."
- Jack-O explaining I-No's origin in Strive story mode, Omen
Thus, seeing this problem, he commented:
"Your conclusion is meaningless."
Now, I believe that this is more personal, since he's now referring to Axl Low. What conclusion, exactly? I suggest, Chaos meant Axl's solution to problems:
"...he rarely thinks about anything deeply and generally goes with the flow..."
- GG World/Axl Low from Strive
You could say that he's the kind of person who focuses on the present, much like Sol, thus preventing them from being torn by philosophical or societal problems like Asuka and Happy Chaos. However, what if said "flow" stopped?
"Please don't stop the flow"
- Drift, Happy Chaos' battle theme in Strive
I think there's a reason why Chaos' song mentioned this line, and that being, the "flow" could indeed, stop. That is, by either letting mankind live through order to the point where they lose their humanity, or by letting the world be destroyed by mankind's emotions. Which are both possible, based on past events and insights that Ariels, Happy Chaos, and I-No gained from the future.
"Mankind will dream. He will prize his purpose. And he will love. Though the robot assumed it was those very urges that comprised a "soul," it predicted that mankind would one day strip itself of any impulse."
- Origin of Ariels' motive, Xrd Rev story mode, Cause A
"His mission is to stir up the world so that humankind does not forget its own humanity."
- A portion of Happy Chaos' description in GG World
"Something has to change. That dull gray world... Time to put it to the test."
"Now time might actually start to move a little in that awful future..."
- Some of I-No's dialogue in I-No's arcade mode, Xrd Sign
"Finally, the day is here. My chance to light up this dull future with amazing fireworks!"
- I-No's dialogue in Axl Low's arcade mode, Xrd Sign
Basically, I interpreted what he said as: "The world needs to be balanced, and you're doing nothing about it."
However, I wondered, "Why did he even have to contact Axl in the first place? Why did Chaos even discussed about scales?" Then, I thought: What if their interaction is actually a "counterweight" in itself? It could be the reason why he brought up "scales" in the first place. So, what is he balancing? What is he preventing from breaking? It's definitely not Sol's presence, since he's already willing to participate the moment they felt that something was off.
Maybe Axl at first, but when Chaos already showed himself the first time, Axl was already guarding the area, anticipating that someone will come. However, he didn't expect that something bad will happen until after that scene, during which, he managed to save people due to his prior knowledge. Was it to save people? Because it seems like that's all it does. But, why? He didn't mind killing off the guards later and letting the soldiers die, why does he seem to care here? Then I realized, he was doing it for a much, bigger picture... The G4.
Interestingly, the US president, Vernon, sounded too optimistic after the incident:
Vernon: Your former ally has been detained by the Illyrian government. It's a real weight off my shoulders.
Asuka: The I-No I know would never let herself be captured so easily.
Vernon: I imagine they're interrogating her right now... So why don't we save the anxiety-inducing conversations for after she's escaped?
- Shortened conversation between Vernon and Asuka in Strive story mode, Omen
I'm guessing this was because, on paper, the incident was handled "smoothly." A building collapsed, but everyone inside was saved by a hero and the culprit was imprisoned. However, when some people did die, they took the matter more seriously:
Goldlewis: What's the damage report?
Operator: Initial reports say 48 police and soldier casualties. But that doesn't account for the numerous civilians caught up in all this.
Goldlewis: Was this a political group? Some single idealogue?
Erica: Illyria tried to warn us. I downplayed the danger because I-No was in custody. These deaths are my responsibility.
- Discussion during their attempt to reclaim the White House, Strive story mode, Myth
Therefore, if people had died in the building, perhaps Erica (and maybe even Goldlewis) will also think twice about continuing the event, and consequently dissuading Vernon. He might even consider Asuka’s suspicion, and wait for further information from Illyria (especially since, they knew about Chaos' existence anyway. I don't even know why the US didn't know that despite knowing I-No's detainment. Plot hole I guess or they relied on the news instead of direct communication?)
In addition, if ever he was too late, Axl cannot go back in time to save those people:
"Well, you are able to access "any" world... So it's not impossible. However! If you do use your...irregular...powers, this world just becomes another possibility. Poof! Gone in a flash."
- Portion of Jack-O's explanation about Axl's power, Axl Low's arcade mode, Xrd Rev
"Two worlds. In other words, the past in which you lived, and the present. Two timelines. By reasserting one of them, the possibility of the other disappears."
- Sol reiterating Axl's dilemma, Xrd Rev story mode, Contact B
Thus, Axl Low can't travel back in time to change the past, or else the entire "present" where he came from will disappear (and somehow that counts as killing for him, which he didn't like). Thus, the most that he could do is to stop time and move alone there, like how he saved the people in the building.
Based on these info, I theorize that Happy Chaos intentionally creeped out Axl in the scene so that he could save the people in the building, which then allowed everyone in the White House to have the confidence to continue the G4, all while hinting about his plan in the same scene.