A membrane will only stop weeds growing up from the soil underneath (or it should do!). However, seeds can still be sown in the gravel by the wind and via bird droppings. The only good thing is, rather than having to dig them up, you should be able to pull them gently out of the gravel, root and all. I have to do this every so often (esp. in Spring) in my garden.
A good cheap method of getting rid of garden weeds on patios etc is to mix a good few tablespoonsfuls of Table Salt with hot water into a jug and pour onto the weeds, but be sure to keep well away from plants. If the weatherman predicts rain, just pour the salt direct from the container onto the patio and let the rain water it in. Doesn't leave a strong smell like weedkiller either.