Rose Tyler isn't sure when exactly she started falling in love with the Doctor, or why. All she knows is, at some point in the past who-knows-how-long since the first nineteen years of her life, she's made up her mind. She wants to stay with him forever.
She isn't sure what exactly it is about him, either. He doesn't have the qualities of the other men or other humans she's known. The Doctor is- well, he's alien, and unfamiliar, and exciting, but at the same time he can be so bizarrely human.
She thinks maybe he's travelled with humans for so long that he's becoming one.
Only he hasn't travelled with humans for long, not recently, anyways. She's listened to the stories the first Doctor would tell her, she knows he took a long break from humans, and some of the things he faced in that period. His humanity might be a reflection of what her wishful thinking- maybe she's just searching for something human to cling onto while she explores all of space and time with him. Or maybe it might be that she has made him more human.
The last thought is one she wonders about, when she's falling asleep after an adventure (you can't exactly call it night when you're a time traveller). Does he feel the same way? Has she really made an impact in his life? She's seen the way he acted around Jack, Adam, and Mickey, heard what Mickey and her mum think of their relationship, but she never really can tell how important she is to him. Yes, he's protective of her, but he's always detached, too, with his sense of humor and his "oh-you-humans" attitude. It's strange to think how he could be like this for all of his companions- immensely important, definitely life changing, and yet, to him, they're just another companion. She's heard a little about his past companions, too. Many of them had never met an alien before him, and yet he's met so many aliens before all of them.
Rose thinks that sums it up pretty well.
When she's thinking like this, she usually goes and watches him at the TARDIS console. Normally, when she's sleeping, they're in orbit somewhere, but she rarely sees him sleep. Either he'll be fiddling with the controls and muttering to himself- "come on, come on, that should work, that worked last time", "oh, yes, haven't been there in a while, let's take her there"- or he'll be leaning up against it, staring into space with his fingers steepled at his nose. Sometimes, when he's lost in thought like this, he looks so- so alien and indescribably old in his expression, that Rose will call his name, just to make sure she hasn't lost him completely. His reaction is the same as it always is when she says his name. He'll smile and look over at her, and in that half second of action, he'll become her Doctor again, all energetic and human. And yet he wouldn't be her Doctor without those times where he disappears into his thoughts, and she doesn't think she would love him as deeply if not for his alien qualities. It's what he is, it makes him a walking contradiction- human and alien, close and distant to her, cheerful and energetic and yet haunted, childish but centuries old, friendly but destined to be alone, well-travelled and still so curious, an immortal alien living in a breathing human body. It's what he is, at the heart of him, one big paradox, and it's why she loves him and would stay forever if she could.
"Doctor?" she says, and he performs the magic act again, becoming human before her eyes.
"What is it?" he says. "You should get some sleep, I've got big plans for tomorrow."
Rose walks further into the TARDIS console. "You know I'm going to be with you forever, right?"
The Doctor smiles at her, but there's still something of the alien left in his face. "I know you would if you could."