I weed for my parents and they have rocks. I'm constantly doing a combo of spraying the vinegar solution and pulling up weeds. My house has all mulch and I never spray and only have to pick very few weeds out every now and then (like a handful). The mulch seems to an environment the weeds don't thrive in.

I apply Sprectacide Weed Killer WEEKLY that i make from concentrate in my pump up sprayer. Mix 8 oz of "Sprectacide Weed & Grass Killer" concentrate (white bottle) with 1 gallon of water in the tank, shake it up and walk around and spray any weeds that you see in your flower beds. This only takes about 5 or 10 minutes a week if you first sprinkle PREEN in your flower beds to significantly reduce the number of weeds that sprout. Preen doesn't kill weeds, but it prevents most of them from germinating, then the Spectracide spray kill the weeds that sprout.

Keep the rocks dry
 

The vinegar / dish soap potion sort of works but it only kills the leaves and not the roots. Without killing the roots the plant will return.
Hand pulling by far is the best method but be sure you get the roots.
As a preventative measure you will see much improvement in weed pressure if you only water the plants you have and don’t just water the entire bed. Drip irrigation is the way to do this as dry rocks or bed is not a very good environment for weed growth. You’ll still get weeds but the volume will be significantly different.

Pinestraw

I put down pre-emergent which does keep the weeds at bay. I also walk around my planting areas once a week with Round Up in a pump sprayer to spray the grass that encroaches these areas. Don’t forget the cracks in your driveway.

Cancer

Look up the Latin and common names of your "weeds". Memorize them.

They are now an integral part of your landscaping. Remember how little they cost! Smile and enjoy the extra time you made available for your preferred activities.

Most people seem to start with mulch or pine straw and switch to rock. Just what I have observed in TV.

Use Preen Products to control weeds in Yard & Garden
 

We've used Preenfor lawns and vegetable gardens for years! My wife loves Preen in her flower gardens. I love applying it in the Spring on the yard. It Really prevents and controls weeds - much better than any Scott's or other products we tried. You'll love it also! Lowe's has it. So does Amazon.

Use newspapers . Take out the mulch lay a thick layer of newspaper down and wet it then put the mulch back on top and no weeds. in a few years the paper will mulch up then do it again.

I use Groundclear. It doesn’t migrate and only kills the plant or grass you spray it on. It’s comes in a gallon sprayer at Lowe’s. I take 10 minutes every week and walk around the grass and hit any weeds, then hit the flower beds for any grass or weeds. Before the end of the day they are already brown. It’s the only way to keep it under control with the least amount of effort. Everyone has 10 minutes a week. Plus no bending over. Pulling weeds is futile because you rarely get all the root and it just comes back. You have to spray them.

Weeds
 

Mulch becomes a breeding ground for weeds when wet or all the time. Pulling out once a week works best

Won’t the torch method burn the landscape mat?

I’m told that using mulch or pine straw is better for keeping the weeds at bay than landscaping rock/stone.

real easy to solve. you need the heavy duty fabric, then you need at least 3 inches of mulch. We use cypress mulch in bulk never a weed since 2006!