AutoCad :: Lineweight Appear Less Thicker After Copy

When I copy objects from a drawing to another drawing in .DWG, it appears that the lineweights becomes different between the two drawings.

For example, let's say there is a layer whose Lineweight is 0.3mm, Color is green and Linetype is continuous on the source drawing file. You notice the objects under that layer should be thicker. After copying to another drawing or destination drawing file, I noticed the layer got transferred across which is good and everything else associated with that layer. But then, I noticed on the other drawing, the objects on that layer are not as thick as that of the source drawing file. When i checked the layer on the layer properties manager, it shows the lineweight is 0.3mm. I wonder why the lineweight of the objects are different as if they are 0.00mm and what should I do to keep it consistent on the other drawing after the copy.