What is the best way to change edge weights on a mesh? [NB: I think this question may have been asked and answered before, but in doing a search of the archived questions and answers, using what I though would have been words contained, I did not come up with any matches.]

Consider this set of images,

,

and assume that I have made a mesh of any one of them in Blender. Is there a simple way to create the other two from the mesh I made, so that I could change the width of the border around the figure? I want to change the width of the part of the mesh shown in black, while leaving the part of mesh shown in white relatively unaffected. Using the scale function seems to change the width of the border at the outer most points of the mesh by a different amount than the border of the elements that cross nearest to the center.
You could use a skin modifier to create the outline. You can adjust the thickness of the skinning with &#9096; CtrlA in edit mode. The properties region N can also be used to adjust the radius.



Make a duplicate of your mesh to use for the outline, in the duplicate delete all the faces and the edges that cross over the pathways so you only have edges where you want the outline to be. Add the skin modifier to this mesh. For each disconnected piece of mesh you will need to mark a vertex as root (use the button in the modifier), otherwise that section of mesh will not be skinned.



Instead of the skin modifier, another option is to convert the outline mesh to a curve object and use the curves bevel depth to adjust the outline thickness.