Not sure I understood the question, but here goes:
To change the color or thickness of an edge in yEd, click on the edge in question to select it, then go to the properties view in yEd's lower right corner. Among other properties, the "General" section has properties "Line Color" (for changing the color of the edge) and "Line Type" (for changing line thickness and line pattern).
If you have assigned custom properties to your edges and you want to change the edge visualizations depending on a specific custom property value, you can do so using yEd's properties mapper ("Edit" -> "Properties Mapper"). Please see section Mapping Custom Properties to Visual Properties in the yEd manual for related documentation.