Can i somehow see and change the vertex weights of the created vertex groups?
Yeah, this is a problem. Most operations of weight paint won't even work if we try to weight paint a mesh that has no faces. If we take a vert string and try to do a weight paint gradient, we won't even get an operator box, much less any change in weights. And that's ignoring the fact that even if we could change the weights, we couldn't see how we changed them.
I haven't found a good solution to this, so here's the best (not very good) solution that I've found instead:
Add some faces to your string and use a mask modifier to get rid of them before the skin. Once we have any faces whatsoever, even if they're being masked away, we can paint weights. We still can't see them, not while the mask modifier is active, but we can paint them.
If we need to see our weights, we can disable the mask modifier temporarily. This is far from ideal, but it's what I've got.
Skin creates an Armature from the edges of a mesh and additionally creates a vertex group for each bone.
You can see and edit the weight of those automatically created vertex groups when you switch the object interaction mode from Object Mode to Weight Paint in the upper left corner of the 3D Viewport.
If you then select a Vertex Group in the Properties under Object Data Properties, the corresponding weight is displayed and you can repaint it.
EDIT: If you want to draw directly on the mesh that the modifier
skin has created (for example, if you used only vertices as a starting point), then you would have to apply the modifier first:
Another way to influence the weights without applying the modifier
Skin is to simply use the Bone Envelopes instead of Vertex Groups.
For this you would only have to change the value Bind To in the modifier of the Armature to Bone Envelopes.