When it all starts, it's to say, at the beginning of everything (well, not everything, but the important bit at least), Aziraphael made every attempt to avoid the snake that lay, lazily, basking in the warmth. It's not that Aziraphael didn't like snakes, quite the opposite actually, thought they were beautiful creatures (like all of God's creations, obviously), and this one was no different, with scales that flickered between a molten orange-red, and black, depending on how the light caught them, large, but not quite intimidating. No, it's not that Aziraphael is scared, or uncomfortable because of the snakes presence, merely that he feels an odd sort of... energy from the snake, which seems awfully strange, but he tries to think very little of the matter and focuses on the garden.
This is probably how the snake is successful in tempting the humans. In all his efforts to avoid the snake, he'd left the tree unguarded.
Once the snake - Crawley - is stood next to Aziraphael on the wall, the determination to not look at the snake - demon - does not falter. It was quite unnatural for Aziraphael to not look at someone who was talking to him. It was really quite rude not to look at someone with whom you were having a conversation, said person should be graced with your full attention. This is something Aziraphael felt quite strongly about, manners. He felt it said quiet a lot about someone's character - whether they said their please and thank yous, if they gave you their attention when you spoke to them... eventually this list would include other things too, like allowing someone to walk in front of you, offering you a lift home in their car, paying for dinner (or lunch), holding a door open...but these things needed to be invented first.
Crawley did not seem to have a problem staring at the angel, his eyes focused on Aziraphael, but not entirely on what Aziraphael was saying (rude!). Aziraphael was quite certain the serpent probably thought him skittish, nervous. But quite frankly, looking at Crawley, black wings fluttering behind him, ink-y black like a ravens, it hurt a little.
He observed, in the few seconds he cast his eyes towards his should-be enemy, the bright almost fluorescent (they weren't, but somehow also were, Aziraphael felt this probably was something to do with the power the demon possessed, because otherwise he wasn't at all sure how else to explain it. Maybe it was just another of those oddities, ineffable) yellow eyes, slit-like pupils seeming to make his gaze all the more enticing (Angels of course do not feel enticed, but Aziraphael imagines if he were a human, that's what he would feel) and the shocking auburn hair that fell down his back.
Aziraphael quickly had to avert his eyes after observing solely those minute details (later Aziraphael would realise that he has every molecule of Crowley memorised, but they had plenty of time for that. Milena).
Their first two encounters are much the same, Crawley seems oddly relaxed for a demon who seems unsure of the point of what is happening (either in heaven or in hell), and gives Aziraphael his full attention, in some way or another, while Aziraphael can barely look towards his...dare he say, companion, stuttering out answers to Crowley's questions, and trying not to preoccupy himself with how unlike himself he's being.
It's not until Crowley arrives, announcing a name change (very minor, and quite frankly a little ridiculous, although Aziraphael will admit he does think it suits him better this way), that Aziraphael gives Crowley a little more of his attention. He's ever so grateful that the demon doesn't seem to realise his slight avoidance. Well, if Crowley notices anything, he doesn't mention it, anyway.
It's just, well, Aziraphael feels guilty, and doesn't really want to have to explain that it's his fault that Crowley made a quick decent down to hell...
That, he's sure, really would "go down like a lead balloon".