Try sewing in a tape or ribbon along the hemline - that will actually reinforce it rather than do damage. You might need to sew the folds into the tape to keep the kilt's pleats sharp

If you need more weight than that you could try adding net curtain weighting strip, which is a continuous tape either with small beads in - which is not the best option, or a smooth strip of plastic-y stuff which can easily be cut into short lengths. You could then put a strip of it along the hemline of the underside of the pleat, or vertically into the lower part of the inner pleat and then sew the fold down to make a narrow pocket from which the tape could be removed for washing.

I am assuming that type of weighted tape is available to you, though if you use the pocket method you could use any small weight, but wrap it to prevent damaging the fabric. A strip of old handkerchief of a thin shirt material would do the job.