You would simply have to apply the vertex group to the points first with Capture Attribute
, and then use that as the selection for Mesh to Curve
:

Here I use the node Named Attribute
(Blender 3.2) for the vertex group, but of course you can also do this with a Group Input (Blender 3.0).
A short (simplified) explanation:
It has to do with "Domains".
A vertex group defines points, but Mesh to Curve
works based on edges.
When you process a vertex group in Geometry Nodes, this selection is interpolated to all other domains, which also selects adjacent edges.
So all edges that have a point in this vertex group will be converted by the node Mesh to Curve
.
With Capture Attribute
, however, the selection is explicitly applied only to the points domain and then only edges are selected that actually have both points in this vertex group.