I used ~6 layers of newspaper one year.
- Planting was tricky. I cut X's in, but getting the seedling in the right spot didn't happen and tearing bits of the paper off to not squash the seedling resulted in a mess. Recommend to cut holes instead. I was worried for seedlings from direct-sown seeds, as I didn't want them to get lost between the soil and the paper and the mulch.
- Water will run off the top, so you must either have watering holes, water directly at the plant base, or run irrigation under the paper.
- I wound up with a dried bubble of paper due to watering through holes between plants, rather than watering from above.
- Runner/Bermuda grass still ran through underneath the paper, and I had some kind of Liriope that would poke straight up through the paper. It did help, but was not entirely effective.
- Side/top dressing with compost or other fertilizers gets much more complicated when you have to move whole sections of newspaper.
- Rain would wash my mulch off.
Next time, I would go MUCH thicker (10-20 sheets) or corrugated cardboard, and irrigate below. I'm not thrilled about watering newspaper to keep it stuck together. And the lack of ease of fertilization all season pretty much trumps the rest.
This year I'm planning on crowding so many companion plants and herbs in the beds there's no room for weeds.

I already picked through my soil to pull all the roots and bits of bermuda grass I could see. Since I prepped the beds I've not really weeded (3-4 weeks in the average 70s with enough rain to keep things damp to within an inch of the surface), and I'm only seeing a few bits of things popping up, most of which is really easy to remove. The grass still sends runners in, which I dig/pull ASAP.