I just saw a gifset of the scene where Rogers asks Tilly to move in and you see hesitance in his face. This scene is often paralleled to Mary Margaret asking Emma to live with her, but there’s a key difference here.
This is a man, who if we go based on Colin’s real age is pushing 40, asking a young 20 something year old girl to move in with him. A lot different than a 28 year old woman asking another 28 year old woman to stay in her spare room.
He knows how this looks. He has to word it carefully, because he doesn’t want to make it uncomfortable or seem like he’s trying to take advantage of her.
Because how many men ask a young girl to come stay with them with no expectations?
He doesn’t want to come across as pushy or seem like he’s being a creep. Because he’s not. He just cares about her and doesn’t want her living in a train car anymore.
And luckily, Tilly understands.