I am not a big fan of fusible interfacing, but it is easy to use. If you really feel they need some extra "support", I would buy some thin muslin (PREWASH IT BEFORE USING as it can shrink a lot), cut it into squares the same size and stitch them to the outer edges of the blocks. But this will add weight to the finished quilt, which may or not be a concern for you.
Keep in mind that the stitching of the quilting will add a lot of stability to those blocks, and of course the heavier the quilting design the more support the blocks will have.
I guess one last thought, is your concern about the thinness of the fabric quality, or the potential for the seams to come undone as the quilt is used? Fusible interfacing may be of more help it the fabric itself is thin, but adding muslin and more dense quilting may be more helpful if it is the long-term fastness of the piecing that you are worried about.