I reside in South Central PA, which is Zone 6b, right on the border of Zone 7a (if you're closer to the City of Harrisburg it would be 7a). It gets hot in the summer, humid hot - there were plenty of 90* + days with high humidity. This past summer (2022), we hardly received any rain. I was watering trees every weekend for about 2.5 months straight, moving the hose from tree to tree sometimes till 11pm at night.
My green giants received an entire summer worth of baking sun with that black weed barrier uncovered. I noticed MINIMAL scorching (e.g. browning) of the cedar foliage, and it was restricted to only the newest (non-established) plantings. I was certainly worried about them burning, but to my amazement (with a record hot/dry summer), I couldn't count on one hand the sun damage amongst 100 trees.
The moisture retention was incredible under the barrier even without top dressing with mulch. For me to mulch 1200 linear feet of weed barrier would be an expensive and exhausting task (I do not own a sub-compact tractor yet). And I say expensive because I WILL NOT use wood chips anymore around my trees. My father is an avid arborist, even in his retirement years. I can get all the wood chips I want, but I have witnessed them doing more bad than good. They steal nitrogen from the ground when the decompose (which steals it from your trees), they grow mold & mildew, fungus, they get matted down, take forever to break down into something organically beneficial for trees...I could go on and on. I only use organic bark mulch for my trees anymore, so for that reason, I'll be leaving the 5 oz. weed barrier uncovered, unless something drastic changes and I notice quantifiable damage. Plus I swear the deer do not like walking on the uncovered mat - which is another deterrent IMO.