It looks like that obj to dwg conversion is in most cases related to a 3D to 2D conversion, something like export of a slice or 2D view from a 3D model (.obj) to DWG graphics. It is likely that this can be done using lots of different 3D modeling tools or even some dedicated converters.
Open OBJ file Open DWG fileA set of 3D modeling tools
3D CAD/CAM tool for product development
A 3D CAD translation software