The video, as a lot of similar Youtube creations, with similar weather balloons, equipped with cameras and some talisman, was named "[fill in your favourite object here] carried to the edge of space"
Of course, at that height one can see the curvature of the earth and the thin line that makes up the atmosphere. But it is not the edge of space. Not by far. And however ingenious and spectacular the videos are I have strong objections calling things like this "to the edge of space".
Because it just isn't.
Why? I'll show you after the jump.
A weather balloon is a kind of aircraft that needs the atmosphere to exist. Without atmosphere there is no pressure and the balloon will expand immediately to the moment it will explode. So therefor it only can exist inside the Earth's atmosphere and not in space. A normal weather balloon is capable of reaching heights of around 30 kilometres. Which is very high indeed. In fact, most of the Earth's atmospheric particles are below that height. It is almost an environment without oxygen, people can not breathe there. But it still is inside Earth's atmospheric boundaries. There still are so much particles found at that height that it easily can be called atmosphere, albeit very thin. Aircraft like the U2, the famous spyplane can go up to these heights only because the huge size of their wings. The air is so thin up there they need those big wings to stay aloft. But the fact the plane's engine still works there, also shows there still is *some* atmosphere left.
Space starts at about 70 kilometres higher. At one point in time some very smart people decided that that point would be where "space" would begin from now on (the Kármán Line). Even then, there still are traces of atmosphere detectable. enough to slow low-orbit satellites down to the moment they re-enter the atmosphere and burn up.
The ISS is found at around 200 kilometres up and it often needs a little boost to maintain that height, because of the remaining particles up there, slowing it down, getting it to lower its orbit. Some satellites even orbit at 36.000 kilometres, to maintain a geosynchronous orbit, This way they are able to keep above the same place over the earth's surface all the time because their rotation is one orbit in 24 hours, just like Earth itself.
Here is a very clear diagram of how high the atmosphere is, how high weather balloons can reach, and where space starts.