I feel like the first "I forgive you" and the second "I forgive you" are different "I-forgive-yous" (or maybe not)
What else "I forgive you" may mean (one year later) — Good Omens Season 1 and 2 parallel
Ok, I know I'm 1 year late to the party and I don't know if this has already been pointed out, but it came across my mind like a lightning this morning, and now I just can't stop thinking about it. We know there are lots of parallel scenes through GO Season 1 and 2, and that we have two "I forgive you" moments. The first "I forgive you" makes utterly sense: Crowley just offended Aziraphale, and he replies with "I forgive you" (despite the demon had said just a few scenes before "Unforgivable is what I am").
The "I forgive you" in S2 left us all stuck in despair, trying to figure out why Aziraphale would have to say that just after their 6000-year-long awaited kiss.
First of all, I want to make clear that I believe this answer is totally in-character: I forgive you for kissing me while leaving me on my own when I most needed you, I forgive you for not believing that we can make a difference together, I forgive you because you are not unforgivable and I'm not giving up on you, I forgive you because forgiveness is love, it's a gift—"forgive" literally translates the Latin verb "perdonare" (per=for + donare=give) and also means "to give without conditions"... and the list goes on and on. I recommend this @sendarya's analysis which I found really accurate and on point, check it out if you haven't already: https://www.youtube.com/watch?v=NOvv0GkMBA8&t=34s
Nevertheless, there may be a second layer of meaning. Let's go back to S1 for a moment. Aziraphale finds the Antichrist, but he chooses not to tell Crowley during the bandstand scene: he wants to sort it out on his own. Later, when Crowley comes to the bookshop to apologize, he just tells him that he wants to talk to God to thwart Apocalypse, which triggers Crowley's "You're so clever! How can someone as clever as you be so stupid?". So let's recap what happens: 1) Aziraphale knows something he isn't telling Crowley and has a plan; 2) Crowley offers Aziraphale to go off together, but Aziraphale refuses because he wants to save Earth; 3) Crowley offends Aziraphale: "How can someone as clever as you be so stupid?"; 4) Aziraphale says "I forgive you"; 5) Crowley leaves (let alone calling Aziraphale again 5 minutes later).
Later, after discorporating and failing in his attempt to reach God, Aziraphale realizes that the only way to thwart Apocalypse is "our side", so he appears to a drunk and devastated Crowley to reveal him that the Antichrist is in Tadfield, and they arrange to meet there. We may assume that, after the Armageddon't, they talked of what happened, and Aziraphale may have told Crowley that he already knew where the boy was during the bandstand meeting; anyway, Crowley saw Aziraphale acting mysteriously and keeping his secrets: he said he wanted to talk with God to sort things out, but nothing more. Crowley knew that there was something his angel wasn't telling him, and that he had a plan. Now let's see what happens in S2: 1) Aziraphale knows something he isn't telling Crowley (he doesn't reveal Metatron's threats) and (hopefully) has a plan; 2) Crowley offers Aziraphale to go off together, but Aziraphale refuses because he wants to "make a difference"; 3) Crowley hurts Aziraphale: "No Nightingales. You idiot. We could have been us" (+ bonus, devastating kiss); 4) Aziraphale says "I forgive you"; 5) Crowley leaves the bookshop... but he just waits across the street, until Aziraphale takes the lift with the Metatron.
Ok, nice parallel so far. But what am I trying to say with that? I think that perhaps—just as "Trust me"—"I forgive you" may have come to acquire a second, coded meaning: "There's something I'm not telling you, but I have a plan". One more, desperate attempt of our angel to tell something to his demon without anyone else noticing, as he knows that the Metatron is watching. Crowley waiting by the Bentley is a way to show his angel he's not giving up on him, but maybe also to let him know he got his message.
So, do what you want with this, now I can go on with my day despite the brainrot (maybe).