Yes in SolidWorks you can assign a custom mass/weight to a part or assembly and then link that information to the drawing through Custom Properties. You are going about setting a custom mass the correct way but now you need some additional steps.
For a part of assembly, select tools, mass properties. Enter the value for the mass.
In the ConfigurationManager, right-click Default. Click Custom Properties.
Select Weight for Property Name. Select from the drop downlist "Mass" for Value. You need to use the SW-Mass
Now create your drawing, use the predefined BOM template that contains Mass. You mass from the model will be displayed.
There is a movie of the solution at
http://blogs.solidworks.com/teacher/...f-materia.html
Good luck. Marie