In "The Dragon and the Wolf" (Game of Thrones, S07E07),
Jon and Dany have sex with each other
It is shown that Tyrion is outside and sees that this is going on. He appears to have a disapproving face.
What is his reason for this disapproval? He doesn't seem to have any reason to be against this.
Tyrion has sacrificed a lot, including loyalty to his family, to be Daenerys' advisor and hand. He believes in her and loves her as a queen and agrees with her vision of the new world she wants to build.
He, along with Varys, has tasked himself primarily with keeping her potential madness in check (indeed, this is something Daenerys explicitly tasked Varys with) - this is highlighted in many episodes but is made explicit in a scene with Cersei in "The Dragon and the Wolf" (Game of Thrones, S07E07):
CERSEI: Eventually, you want everyone to bend the knee to her.
TYRION: Yes.
CERSEI: Why?
TYRION: (PAUSE) Because I think she will make the world a better place.
CERSEI: You said she'd destroy King's Landing
TYRION: She knows herself. She chose an advisor who would check her worst impulses instead of feeding them
—"The Dragon and the Wolf" (Game of Thrones, S07E07)
Tyrion strongly believes in Daenerys' "better place", but also has expressed deep concern (sometimes even hints of regret) about the things she does (when he watched Drogon burn the Lannister troops, or when he walked through the field of ash, or when he tried to stop Daenerys from burning the Tarlys).
He already recognised this problem with the Jon-Daenerys romance at Dragonstone, in "Beyond the Wall" (Game of Thrones, S07E06), when he saw Daenerys risk everything (her own and her dragons' life, along with any hope for a new world) at the first mention of Jon Snow being in danger.
Seeing Jon Snow entering her quarters (and correctly inferring that their romantic/sexual tension had come to fruition) struck him with deep concern because now he knows his own influence to keep Daenerys' worst impulses in check has been compromised, and moreover Jon will be able to influence her, or have her risk her life again whenever he is next in danger.
Out-of-universe it is supposed to echo the concern going through the audience's mind, as we (watching this scene narrated by Bran) are experiencing the dramatic irony of this sex scene, and are having our own reservations about an incestual sex scene between an aunt and nephew, and are having our own thoughts and concerns about the political and romantic strife this will cause later on, when they find out. Tyrion's expression of concern serves narratively, but also out-of-universe to echo our own concern.
In Game of Thrones: Cast Commentary on A Union of Fire and Ice (HBO), Peter Dinklage, the actor who plays Tyrion, comments on this very scene and gives some insight into why he reacts the way he does:
It's dangerous for everybody involved. I'm sure it's good for both of them in the moment, but ...
You don't even get the relief of how beautiful it could be or should be, it's ..."No! It's not good!". But it should be, "but it's not!".
It's Game of Thrones - there's a long history of romance not ending well on this show.
—Peter Dinklage, Game of Thrones: Cast Commentary on A Union of Fire and Ice (HBO)
Isn't it uncle and niece? No.
Commented
Aug 28, 2017 at 10:36
Although an excellent answer is above, The New York Times posted an interview with Director Jeremy Podeswa today. He directly addresses this question,
When Jon and Dany hook up, we know it’s incest, but they don’t. So why does Tyrion look troubled? Why the reaction shot from him?
From my point of view, Tyrion always seemed three steps ahead. As long as there is a professional alliance between Dany and Jon, that’s something that everybody wants. We can imagine that that’s a helpful alliance. But when things get personal, then people make decisions based on their emotions, and that can complicate matters going forward, so I think he sees the potential here for things to get very messy. Usually, historically, nothing good comes out of relationships becoming more complicated! [Laughs] It’s also a question of what’s going to be his role within this new alliance, right? So there’s a kind of caution here.
I believe Tyrion knows about Jon's parents.
That is why he looks so confused. On one hand, he wants a next in line for Daenarys, on the other, he feels this is wrong, especially because they (Dany and Jon) don't know. Unlike Cersei and Jaime did.
How
Varys told him...
How does Varys know? In season 1, Varys visits Ned Stark a few times in his cell. On the last visit, Varys informs him that they will let him "take the black" and live out his days with his bastard son if he pleads guilty and asks for mercy.
Ned asks for one last favor and asks for ink and paper. In 7 season, it has never been revealed what was in that letter or to who it was written too.
He most likely wrote it for Jon or about Jon, so that he didn't take the truth with him to his grave.
Why would he risk this with Varys?
After 7 seasons, that letter is forgotten by most viewers so that it will have enough shock effect when it is revealed.
Varys trusts Tyrion, so it would not be such a surprise that he told him.
But why would they keep it a secret?
They have no proof other than Ned Starks letter.
They have no reason to reveal this to either Dany or Jon, it could only bring internal disputes.
Why
If Daenerys has to hear this truth from a crippled boy with visions and a drop out maester who is in the Night's Watch, she will be skeptical about it, like she is about everything without proof.
But if 2 of her trusted advisors confirm this news, she will be more open to the truth.
Varys was also the Spider when serving the Mad King, he most likely knew the truth behind Rheagar and Lyanna's relationship and might even know about their secret wedding.
Let Howland Reed visit Wintefell at that same time and confirm that Ned came out of that tower with baby Jon, and all the North will believe it too, because everyone knows the story of how Ned killed Ser Arthur Dayne with Howland Reed at his side.
The big "Jon is a Targaryen" reveal must be well supported, not just to convince Dany, but everyone who is convinced before it is revealed is one less doubter and easier to explain why they will all accept this story as truth.
