You have to remember that The Doctor and River encounter each other in "reverse" order. The first time the Doctor met her, was River's last time they saw each other, and vice versa.
The Doctor is sad because he knows for a fact that it's the last time he'll see River in that incarnation. In fact, the next time they meet each other, according to River's timeline, will be in the episodes Silence In the Library / Forest of The Dead, which is a Tenth Doctor adventure, in Series 4. In that episode...(SPOILERS AHEAD)
River sacrifices herself to save the Doctor and all the people in the Library. That's her "death", so to speak, and the Doctor is sad about that.
From the script of Forest of The Dead (emphasis mine)
RIVER: Funny thing is, this means you've always known how I was going to die. All the time we've been together, you knew I was coming here. The last time I saw you, the real you, the future you, I mean, you turned up on my doorstep, with a new haircut and a suit. You took me to Darillium to see the Singing Towers. What a night that was. The Towers sang, and you cried. You wouldn't tell me why, but I suppose you knew it was time. My time. Time to come to the library. You even gave me your screwdriver. That should have been a clue.