Part of my garden has a weed membrane covered in small stones for decoration.  The membrane does very little to stop weeds.  I heard that a vinegar solution kills weeds, though there doesn't appear to be general agreement as to when you can pull the weeds after spraying.  As it's now rainy season, would it be worthwhile to use the vinegar solution and then cover the weed area with clear plastic, so that the sun would still help, then pull the hopefully dead weeds after say a day or two?

Boiling water will kill weeds faster than vinegar. It's pretty much instant for the leaves, but you need to wait a few minutes for it to soak into the soil. Neither will kill the root system of deep weeds unless you dig the ground over so the liquid can make contact with the roots directly. You can also make a vinegar, salt and boiling water solution, but you risk contaminating a wider area with the salt if you aren't careful, and as it will still only kill on contact, I've never seen the advantage over just using boiling water. 

Covering it with clear plastic will just create a polytunnel and encourage seeds to germinate. If you want to cover it, use thick black plastic to heat up and destroy any seeds on the surface without letting light through. If you laid the plastic down a few days before you would preheat the soil and help to dry it out, which would make boiling water more effective below the surface.

 

I'm very grateful for the help.  I see what you mean by the polytunnel effect.  I think I will try and use the thick black plastic idea you mentioned 😊

I don't know how easy it would be to find here, but in the UK, I used old carpets or rugs turned upside down as weed suppressants. They last much longer than plastic. But they are easy to come by in the UK, and not so common here I think.