Balthazar, when meeting another angel, mentally defaults to familial relationships. Chances are he was bound to think of Azazael as a sibling no matter what. He's mentally adopted Aziraphale, as well, and probably Belial and Crowley are next.

"The stars are strange in the Nexus," he says thoughtfully. "Do you suppose he knows all the stars everywhere?"

Ohh. He's touched, and delighted, by the parallels being drawn between him and Azazael, and breaks into a dazzling smile. "I was actually under Gabriel, in my world, until he left Heaven, and then I was passed to Raphael's hosts. See, you understand, then, what it's like to be surrounded by all these incredible details of Creation and just drunk with all of it. I cried for hours the first time I saw all the little hairs on a spider's toes, they're so darling. I was quite young then, mind you, but still."