More information, please, on this "black weed barrier."
If it's plastic sheeting, the soil is being partially solarized (heated) and may be too hot for the roots of these plants.
Also, there may not be enough of an air exchange, especially given the extended rains in your region this season, to keep the roots healthy. Roots need air just as much as leaves do. Weed barriers, whether plastic or "geotextile," work on the principle of denying air and sun to the soil in order to keep weeds from growing through.
Side note from working in my MIL's yard: once weeds *do* grow through this stuff, esp. the geotextile kind, pulling the weeds up is a real pain in the patootie. You end up pulling the weed plus about 3 sq. ft. of weed block, stretching the "approved" holes, where your other hand reaches underneath to get the rest of the weed, etc. I'm just about ready to start removing the weed block from her yard, section by section, so that I can do weeding.
Back to your plants: I think it's much more likely that the rainwater is unable to properly evaporate, that the soil cannot breathe, etc. The wood chips on top of the weed block may look nice, but I personally don't know of any biological function they're serving at the moment other than to complicate the respiration cycle. Nitrogen-robbing sounds unlikely in view of the separation of the wood chips from the soil by means of the weed block plastic/geotextile.
Sunset Zone 17, USDA Zone 9