By default, labels have a transparent background. If that hampers readability, change the label background to an opaque color.
As an alternative, do not place your edge labels on the edges but next to them. yEd even comes with automatic label placement ("Layout" -> "Label Placement" as well as integrated labelling in "Layout" -> "Hierarchic", "Layout" -> "Orthogonal" - > "Classic", and "Layout" -> "Tree" -> "Balloon"). The label's "Preferred Placement" property determines where the algortihm's place the label.