In the Game of Thrones Season 6 Episode 1 "Red Woman", when the Night's Watch brothers take Jon Snow's body into a room, Davos paused to see the blood stain. It looks like he is observing something. So is there something to notice or I am just reading Davos body language too much?
Simplest answer is, he's in shock, head spinning, trying to make sense of what happened and his place in it. Don't forget that, despite not knowing Jon very well, Davos was with Stannis when he personally warned Jon about Alliser and his other enemies.
Stannis: You have many enemies in Castle Black. Have you considered sending Alliser Thorne elsewhere? Give him command of Eastwach-by-the-Sea.
Jon: I heard it was best to keep your enemies close.
Stannis: Whoever said that didn't have many enemies.
Davos: He [Stannis] sees something in you. Might not be apparent from his tone, but it's the truth. He believes in you.
As you can see, they practically laughed off the risk, and Jon didn't follow Davos's advice.
Suddenly, now, it just got very real.
There are some other reasons why what happened to Jon had personal resonance to Davos - more detail on them in my answer to Why does Davos care about Jon so much?
There are other little practical things he could be deducing, too, for example:
- No evidence of a struggle or a fight - he can see that Jon wasn't able to defend himself
- It's probably possible to tell from the blood being frozen that whatever happened was long enough ago that Jon's survival chances are almost zero
- He'll also be aware that he needs to make a big decision about what he does next and who he sides with
It'd be out of character for him to be thinking in such a detached way, but he is observant and quick thinking, and thoughts like this would be buzzing around his head alongside everything else.
Can't blame him for taking a moment to try to make sense of it all.
Ser Davos believed in Jon Snow and his ability to lead the Night's Watch. That blood stain looks like a blurred crow (which is of course bloodstained) which symbolizes that Ser Davos thinks that the Night's Watch is about to collapse now that their only efficient leader has died (The crow is the symbol of the Night's Watch). This is a piece of art and is really open to interpretation. This was my interpretation.