Oh good lord this is gonna be a long one. Most of my favorite lines are from later in the story so they might be spoilery but these are the ones that really stuck with me the most. Also not really dialogue, mostly narration, but I guess it counts too.
"The Panoptes swallows the knot in his throat, and ponders the value of his own words. The warmth that an earnest confession can bring. What does one lose in baring one's heart? At that moment, he couldn't think of a single thing." (Chapter 18)
"Each fear has a temperament of its own, and a song which soothes it and it alone" (Chapter 18)
"May you live long enough to toil and cry out, but never for long enough to enjoy any fruit of your labor. May your lineage perish, and may this world die with it." (Hinterlands 3 - there's something about all the vitriol in the Tapir's monologue here that really gets to me...)
"I wanted to hold him. I should, could, ought to - but it was one of those moments where one resigns himself to whatever sorry fate being a man asks of him, even when he knows it's for the worst." (Hinterlands 5)
"Grandpa sold his soul to the devil for love, didn't he? People died because of it - and so did he, when the weight of his wrongdoing became too much. [Storm] was looking at me with his sweet eyes, hands fidgeting as he waited for my reaction. [...] Guess it's true what they say: the road to hell is paved with good intentions." (Hinterlands 5)
"Is this really what you've sent my way, God? Must I follow the same path my grandpa did? I breathed in, held it... And as soon as I let it out, I knew exactly what kind of death awaited me" (Hinterlands 5, again. The hopelessness and resignation in this scene just hits so hard to me. In all honesty I could get this entire chapter tattooed permanently into my skin)
And last but not least,
"If anything, I think bein' gay is cool!" - (Storm, trendsetter and ageless icon)
There's a bunch of other lines I'd put here too, but for some I don't have a save to reference the full thing quickly (like the "Will I ever turn to stone?" narration from the parking lot scene) and others have very explicit spoilers (like. Every Argos narration from Ruthless. God, why is Argos such a walking spoiler...) so they're left out for now. Also, honorable mention to the hummingbirds that just won't leave Asterion alone