So remember in the stake-out scene with Rogers and Tilly, where they’re in his car watching for Eloise, and Rogers gives Tilly a marmalade sandwich and she’s like “Aw thank you!” and then adds “For everything”?
Right after Tilly says that, the next shot shows Rogers like this;
His mouth is moving, slightly, but we don’t hear him say anything. It’s a bit too open to consider any other reason but of him speaking. It looks like he just said something, or was about to, until Tilly adds “For caring for me, letting me stay with you”.
And you can’t convince me that, especially with the movement of his mouth and jaw, he was saying “Everything”. As if repeating it to her, when she thanked him for everything. But for whatever reason during editing of the episode, they left that off.
So now I go into thinking, because legit he might not have considered that Tilly would think he deserved gratitude. And I don’t think it’s because of any humility, but because of how he didn’t see helping her as a bother or a chore.
He had spent the entire duration of the curse feeling a void in his life; the void left by not remembering he had a daughter he loved more than anything. And when Tilly came into his life, especially when he invited her to come live with him, he didn’t feel that he was going out of his way to do it, because now he could finally feel complete, he could finally feel happy. He wasn’t lonely anymore, his life wasn’t empty. He had someone. He appreciated having Tilly’s company so much that when Tilly said “Thank you for everything,” he was confused because he hadn’t realized how big of a thing it was, for him to take that young woman and offer her a place to stay with him - especially since he let her keep staying with him after the serial killer that had targeted her had died.
He hadn’t asked Tilly to come live with him because he felt he ought to, he did it because he wanted to. And again, when Nick died, she continued staying with him because he still wanted her there. So for him it wasn’t a matter of a favour to her. But Tilly, being the sweetheart she is, thanked him anyway.