It would be ideal to remove as much of the weed barrier fabric as possible sooner rather than later, since the longer it stays in place, the more potential there will be for root tangling (with desirable plants) and weed establishment (for those that will be hard to dig out, if you avoid herbicide). Weeds can grow on top of weed barrier materials as soon as enough organic matter (decomposed mulch, windblown soil, etc.) accumulates on top of it, so its usefulness for long-term weed control is limited anyway. Granted, it will be a tedious, difficult task, to wrangle it out at this point, but any tree, shrub, and perennial roots in the area will benefit from its removal.

Miri