Most of the bags I make are from drapery or upholstery fabric which has more body than regular quilting fabric and therefore don't usually need additional stability.
One that I made I used the fairly lightweight drapery fabric for both the lining and the outside. I really liked how that one worked out.
The only one I've done that I felt was extremely floppy was one that I did not add interfacing with just regular quilting fabric. If I did that again I would probably use either a mid weight interfacing or try out fusible interfacing which I haven't used on anything yet. P