Watch towers don't seem to do anything at all.
I built a watch tower at every single outpost plus main city. I didn't really notice a difference so I deconstructed a watch tower at one of my outposts. Then I advanced one turn. No difference in vision range. I rebuilt the watch tower again and after it completed there was no change in vision range. I then advanced one turn just in case it was one of those things that doesn't become available until the next turn. No change in vision range still.