It would make the process a bit easier I am aware of face-select mode but I don't like the way that works. I would like to be able to weight paint across all faces as I normally would without either weight or vertex selection but with my edges more visible. I am aware of wireframe mode but... obviously that does not give you the visual cues you need for weight painting.
The accepted answer works, but the Wireframe option remains visible both in weight paint and object mode. This means it adds a wireframe overlay for every visible object in your scene. The Show Wire option performs the same function as Wireframe, but it is only visible on objects in weight paint mode.