Since weed seed blows in from the top, landscape fabric does nothing to prevent weeds from growing. Landscape fabric is worthless and the longer it's on the ground, the harder it is to remove. Use mulch. Natural color only.

Here's a good article on why landscape fabric is garbage: https://conservationgardenpark.org/blog/354/why-weed-barrier-fabric-is-a-weed 

Good question! Landscape fabric works well to separate hardscape layers such as a crushed stone base for a patio or path from the soil beneath it, but that is its only real use. In something like 15 years here on the GW (now Houzz owned) forums I have read one person who had used landscape fabric in planting area for more a very few years and was still pleased with it.

It needs to be totally covered to not break down in sunlight, and flapping gray edges are unattractive. Weeds root in from above from wind blown seeds and below from roots that were preexisting or that crept in from the lawn. It makes weed removal more difficult because the roots become entangled in the fabric. Landscape plant roots also get entangled in it as the roots search for the water and nutrients and oxygen that don’t move well through the fabric. It needs to be removed/cut back in order to plant. The soil loses organic matter that helps keep it healthy since the landscape fabric segregates the mulch from the soil, and then as any existing soil organic matter breaks down, there is nothing to replace it, so soil typically becomes compacted and less able to hold moisture as well as less fertile.

As GG48 said, a good layer of mulch works as well and is much easier to remove weeds from, and it will slowly break down to improve soil tilth. I also like planting densely since many weeds need light for the seeds to germinate, so use a dense groundcover if you like your plants separate or invest in a scuffle hoe or light rake to scuffle up the mulch to expose weed seedling roots. Edge beds well to keep them separated from the lawn and any grass or weeds that might try creeping in from there.

For now since it sounds like things are a bit out of control, see if you can hire a teenager to work with you for the summer. Weed an area and mulch it the same day, and then move on to another area. Once everything has been weeded and mulched, keeping it tidy is a matter of putting in some time while any new sprouts are still small so that weeds don’t have a chance to flower and go to seed. If it is still out of control, consider hiring ongoing help or returning beds to mown areas so that there is a size of garden that you can comfortable manage with whatever resources of people, tools, or energy you have available.

When it comes to explaining why one should not use landscape fabric for weed control, GG and Babs pretty much covered the topic. I'll add a personal note. Once upon a time, an energetic gardener laid down roll after roll of landscape fabric in the mistaken belief that his/her weed problems were over. A few decades later, another gardener launched his ambitious landscape renovation only to encounter the previous gardener's landscape fabric. But the fabric was no longer in its original intact state. Instead, years of UV radiation had weakened the fabric to the point that it had fragmented into millions of small patches and even single threads. Now, whenever the current gardener prepares a new area, he spends more time separating the fabric from the soil than on any other aspect of the project.

What to use instead? (1) Mulch. New weeds are easily pulled out of a thick layer of shredded bark mulch. (2) Dense evergreen ground cover. It's a persistent weed than can survive a suffocating blanket of e.g. Asian jasmine. (3) Foot traffic. Create paths by walking through the garden. The soil will be so compacted not even beggar's lice can germinate. (4) The old-fashioned way. After a soaking rain, get out there and pull those weeds up by hand. Compost them if they haven't gone to seed.

Since you invited us to rant…Whoever came up with the idea of marketing a cheap polymer as a boon to landscaping ought to be hung by the #@&*! Every time I dig up a shovel full of frayed landscape fabric that has to be separated from the soil, I want to @#$% the ever living &(_^# out of that %@(&!

I think that about covers the subject forever.

I have three layers over most of my garden with roots of plants between them all. It didn't work the first time so it was done two more times and also right up to the trunks of all trees and shrubs. Ivy and blackberry running between. Another problem is the gravel with bark mulch on top. I really felt the need for a little rant today.

Three layers? How horrible.

because I know landscapers personally who have spent hundreds if not thousands of hours pulling weeds out of landscape fabric. It may keep them from coming up - it doesn't do that either in our yard, but when weed seeds land on the dirt/sand they root in so well into the fabric good look to anyone in the future of your home trying to pull them out. It's a nightmare