He doesn't know why she stays here.
There's little for her to do; he can hardly send her out into the field like the others. He's been trying hard not to imagine the conversation Anya would have with some frightened pre-teen Slayer; some situations call for more tact than he thinks her capable of.
Giles knows better than to think Anya's new, more subdued demeanor means that she's any more diplomatic than she's ever been. She's still Anya; she's just--like the rest of them--more than a little broken.
Giles feels at least a little responsible for her, just as he does for the rest of them,so when she followed him and Andrew to London, he couldn't suggest she might be happier elsewhere. He simply put her in charge of the re-formed Council's finances, a job she performed well, but with surprisingly little enthusiasm.
He doesn't need Andrew's rambling speculation--which made them all sound rather like some wretched soap opera--to know that Anya and Xander had been coming close to some sort of reconciliation in those last few days in Sunnydale. He doesn't have to ask her to know how deeply she must be grieving; he remember too well what it feels like to have someone cruelly snatched away from you just at the moment you'd begun to believe that everything was finally going to work out between you.
Andrew tries to cheer her up, but Giles knows they can't cajole her into getting over this. She'll recover, but in her own time.
Giles doesn't try to drag a smile out of her, but he finds himself keeping near her in his odd free moments, his presence intended to remind her that she's among friends, and she doesn't have to endure this alone. She remains stubbornly withdrawn; there's no talk of her days wreaking vengeance, but she seems determined to set herself apart from the human race.
He counts as a small victory the night when Anya lectures him at great length about the claims some of the others have turned in against the Council's expense account.
He considers it a larger one the night when--after another diatribe about getting receipts from Willow and Kennedy before paying their travel expenses, and yet another shared takeaway meal in the conference room next to his office--she breaks down. Eyes bright with tears and fury, she insists over and over that she hates feeling like this, hates being human, hates caring, but most of all, hates Xander for being dead and leaving her to feel like this.
Even when she calms down, she doesn't try to convince him she doesn't mean it, and he admires that honesty. She won't mean it forever; that's one of the lessons experience has taught him. But experience has also taught him that right now, it's absolutely true. He'd tried to bury his anger at Jenny, to channel it into his--every bit as real, and far more palatable--fury at Angelus, but it had still been there.
Until one day, it hadn't been. He tells her that, but she thinks he's lying, or at the very least mistaken. He can't convince her otherwise.
Giles doesn't know whether to count it as a victory or a defeat, the night Anya turns up on his doorstep, her mouth crushed desperately against his before he can get a full sentence out. It doesn't cross his mind to turn her away; he's wanted her for too long. And for a while, she even seems like her old self, impatiently ordering him to undress and providing a critical--though mainly complimentary--appraisal of his physique.
Once they're in his bed, though, she goes quiet again, and Giles knows it isn't him she's thinking of.
But one of the other lessons he's learned is that in this world, it's best to settle for what you can get, no matter how far it is from what you want.
He doesn't let himself wonder if it'll ever be just the two of them. If he has to share her, at least it's only with a ghost.