I am no insider and cannot help you with the details, but it is pretty clear that there are different quality levels of canvas, same as there are different quality levels of wool fabric. Quality most certainly does not only depend on the kind of material used, but the raw material quality, the weaving and any other treatment.
Furthermore, the canvas is not a solid piece, but typically consists of multiple layers, and each of the layers may also be darted in certain places as to achieve a more three-dimensional contour. How the canvas is stitched to the outer layer should also play a major role.
As far as I know, the type of canvas in high quality suits has to be matched to the outer fabric properties.
Most likely the cheaper tailors use a stiffer and heavier canvas to be able to "stabilize" even cheap and flimsy outer fabrics. As usual, light and strong (canvas) should be more expensive than heavy and strong.
That said, I do not think that "full canvas" in itself, much like "goodyear welted" is a quality indicator per se. It all comes down to material quality and production methods. A glued suit with a high quality interlining might be better than a cheap full-canvas suit (but will likely also cost more in production).
From my (limited) experience, Kiton (together with my current favorite Regent Germany) really excels in terms of light and flexible, yet shaped jackets.