I'm no tailor, but I can think of a few options.
Firstly, make them removeable. Depending on the style of kilt this would be easier or harder. Frankly, if you wanted to do it, this seems the only "safe" way, because if you do this on a contemporary kilt that get's put in the washing machine, I think it might just tear it apart.
Secondly, maybe add a band of some sort of light reinforcement along the line where the weight would hang.