From PHB about the weave...
-"All magic depends on the Weave, though different kinds of magic access it in a variety of ways. The spells of wizards, warlocks, sorcerers, and bards are commonly called arcane magic. These spells rely on an understanding— learned or intuitive— of the workings of the Weave. "
So no, a sorc is just as dependend on the weave as a mage... the diffrence is simply, mages is theoretical, and sorcerers is practical... to give you a example why all casters more or less have to have a sense of magic, if this wasent the case, then casters wouldent be able to sense magic in the first place, or how do a caster learn a spell, if they cant sense magic to begin with ?... its sorta the chicken and the egg dilemma...
The one exception to casters not using the weave or by passing it, would be runelords, or magic users before the weave... simply explained if casters today use program language, a runelord/lady would use machine code, or what program language is made up of... thats more or less the simplest way i can explain it lol
i think you can refer the website as below, see the chapter "raw magic" and "unexplaioned powers"
https://www.dndbeyond.com/classes/sorcerera sorcerer is trying to control his/her inner power, dredge and release the power from his/her body.
if a sorcerer can not control his/her power that is growing stronger and stornger in his/her body to accompany his/her growth process, the sorcerer will die.
in early access of the game, my sorcerer has the above very serious dialog choice with gale after the battle of the harpys.
