Sew?.. you can make a round tube and line it with some old political signs as stiffners.
then as the British saddle bags do .. a cross brace of a hardwood dowel is the support for the straps . weight is a function of the fabric used,
and the features you want to add..

Then again Ortlieb makes Office bags and their Downtown bags,
the shape is squarish , but they mount them at an angle,
so heel strike is less of an issue. and stuff stays dry in them.