How effective are home made weed killers? (vinegar/salt/dishwashing liquid) ?

I recently purchased a home with an in-ground swimming pool. The area around the concrete decking is covered in pebbles, which are on a base of the black plastic sheeting. I am guessing that the black plastic is breaking down and now weeds are sprouting up everywhere. Right now I don't have the time to pull up all the rocks and replace the black plastic.....so I am trying to kill the weeds until I can. It is quite a large area, so it would not be time effective to pull the weeds by hand (which I have been doing some) and it would be VERY expensive to spray with a commercial weed killer. Any suggestions?????