So, I have an edge loop weightpainted and I want to move that edge loop's vertices by their relative weights, How can I do that?
I skimmed through the blender's official documentation and I found a solution, maybe there is another one and you're welcome to post it!
So the way I did it is by using the lattice modifier, someone wondering and not knowing a way to do it might find it useful
Add and scale a lattice however you like, I scaled it enough to contain the mesh (Object Mode):
Add lattice modifier to the mesh you're trying to transform
Input recently created lattice as an object in the modifier's object field and the vertex group you're trying to transform in the vertex group field.
Then select the lattice and switch to edit mode, transform the lattice and the vertex group will transform according to the lattice.
My reputation here doesn't allow more than to links, I'd love to be more illustative by the help of images.