I think there is one thing being overlooked here and that is; gardening is quite physical. Unfortunately a certain amount of hard graft is required and weeding paths is part of it. The best solution to the weed problem is regular hoeing or shimming off. Of course some will say, “but I don`t have time”, to which I will reply; reduce the size of your plot or get somebody to help out. I would not advocate weed suppressant membrane or wooden sides to beds, raised or otherwise, as these only create work in the long run.
Cheers
Pete