I raid the trash cans at carpet shops for jute backed carpet. I use it between the trellis rows so very little weeds to pull. Beside you are kneeling on carpet to work. Much easier on the knees. The roll it up and reuse next yr.
I;ve used old carpet before, worked really good except when I was done with it, it was hard as hell to get up!
I lay down cardboard.
Whenever we get packages, I strip off the tape and break up the boxes and lay them in the garden on the walkways.
They eventually breakdown and condition the soil, too.