DnD Head Canons

[PairO'Dice Lost]

*The weave is not the source of magic in Faerun/Toril/Abeir-Toril/Realmspace, but merely stabilizes that place's naturally wild magic and makes it safely usable

That's canonical, actually. Regarding the "the Weave is just the interface" part:

Mortals cannot directly shape raw magic. Instead, most who wield magic make use of the Weave. The Weave is the manifestation of raw magic, a kind of interface between the will of a spellcaster and the stuff of raw magic. Without the weave, raw magic is locked away and inaccessible--an archmage can't light a candle in a dead magic zone.
[...]
The Weave is the conduit spellcasters use to channel magical energy for their spells, both arcane and divine. Finally, the Weave is the fabric of esoteric rules and formulas that comprises the Art (arcane spellcasting) and the Power (divine spellcasting).

And regarding the "wild magic" part, well, the actual goddess of magic in Realmspace is (meant to be) Lurue. Hints and tidbits of that have shown up in FR novels and some splatbooks (mostly AD&D ones) over the years, and Ed Greenwood has expanded on that several times in interviews, such as:

Originally, Lurue WAS magic—before Julia Martin added the name “Weave” to my GenCon explanations of ‘the great web of magic that’s everywhere in Toril, binds Toril together, and IS Toril,’ Lurue was the embodiment of the Weave.
[...]
The TSR designers quite rightly (given the humanocentric core of that version of AD&D, with its level and power limits on non-humans) wanted human gods to be front and center and of the greatest power and importance, so Mystra (most important to intelligent creatures trying to USE magic) became also the Guardian or Mother of the Weave, and Lurue sort of . . . danced sideways. To become the awe-inspiring mystery she is now.