Suggest you rake back the mulch and lay down heavy cardboard instead of black sheeting. The cardboard is free at recycle stations, grocery stores, etc. Worms love cardboard and will make a beeline for the soil beneath it which will improve your soil health. Spread the mulch over top of the cardboard and let nature take it from there. The mulch + cardboard will smother the weeds and has the added benefit of being cost free. Weeds will grow through the black sheeting making them even more difficult to pull.

I agree with Gardenweed. I use cardboard with about 5 inches of mulch on top and renew about every 3 to 5 years depending on the particular garden. (I don't usually bother to rake back old mulch, just add a cardboard and a bunch more mulch on top.) The black fabric gets weed seeds on top of it and their roots grow into the black fabric. If the mulch isn't thick enough, it gets loose and flaps around. You will still need to do a small amount of weeding, but the mulch will make it easy and quick and prevent most weeds. I tried the black fabric back when I was a newbie and regretted it for several years until it had all been removed. (If you do a search on landscape fabric on the perennial or shrub forums, you will find lots of people giving the advice to not use it.)

By the way, your English is perfect - no need for any apologies at all.

I agree with the advice above, and would add that you can use newspaper instead of cardboard - it can be a little easier in some situations. You need the paper to be a minimum of 3 sheets thick, more is better.

In her garden book 'Trowel & Error,' author Sharon Lovejoy recommends you "March with the Times"--the New York Times that is and use 30 thicknesses of newspaper under mulch. I found even that many layers disintegrated within a year and didn't stop dandelions or violets from pushing up through. I switched to recycled cardboard because it seems to deteriorate more slowly and smothers/suffocates the weeds better. Both attract worms to the soil.

Thanks very much for all of your responses. I will try cardboard instead of black sheeting. Also, thanks for the detailed instructions. Now I know how to do that. Thanks again!