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To her, he shows up randomly. The first meeting is perfect in her eyes, and years later when she tells him about it, she realizes why. He hadn't been there for it yet, he just does what she told him he did.
The second time he ends up giving her a dairy that he tells her he had specially made on the fifth moon of Poosh, he mentions how the sixth moon is the one that was lost, and he tells her the story of the DoctorDonna. The young River Song isn't as hard or jaded as she is in the future, and hangs on his every word.
He makes her a sonic screwdriver, teaches her how to use every setting on his.
He calls her Dear and Sweetie and Honey, and she swoons just a little bit every time. He smiles, because he knows what's ahead for her, and that's just a little more comforting than he thought it would be because he's teaching her every little thing that she needs to know to keep her future and his past on track.
He shows her how to drive the Tardis and opens the doors by snapping his fingers. He makes a joke about leaving the parking break on when he was younger, and knows one day when she repeats it in his past and her future it will drive him mad.
There are so many secrets he shares, words he says, stories he tells. He tells her about the universe's biggest library (A place he knows where she will one day meet her end and beginning) and about the Pandorica (a legend that isn't real, but he must tell her about anyway because at the time she knew about it- only he can tell her about it if it doesn't truly exist). He takes her to see places she'll one day introduce him to and do things that will one day save the world; he buys her first tube of psychotropic lipstick for her as a present.
By the time he takes her for the picnic, for the last time he'll see her linearly and the second to last time for her, she's more than a companion or a friend. Not quite love, but respect and admiration, for sure. He knows exactly what is in her future, and for the first time that's more than a little upsetting.
To him, it's preserving the timeline. It's teaching her everything she needs to know for her future and his past. If she happens to fall in love with him just a little, than all for the better. He knows her future, and she's going to have to trust him for it all to work out.
To her, it's love.