Maxperson
Morkus from Orkus
Not according to 5e. According to 5e the Weave is just what the local FR folks call their source of magic.No,,, "The Weave" is a specific & fairly deep bit of FR specific lore linked to FR specific gods through that FR specific lore. Magic on Athas is extremely different and those differences are a big part of the setting.
"Mortals can't directly shape this raw magic. Instead, they make use of a fabric of magic, a kind of interface between the will of a spellcaster and the stuff of raw magic. The spellcasters of the Forgotten Realms call it the Weave and recognize its essence as the goddess Mystra, but casters have varied ways of naming and visualizing this interface. By any name, without the Weave, raw magic is locked away and inaccessible"
It's right there in black and white on page 205 of the PHB. It has different names and ways of visualization. It's simply the local setting's source of magic. Not the Weave across all worlds.