The consensus is that you do not need weights. That they will do more harm than good. As was said before, they will constantly be hitting on your legs as you walk and will form hard spots in the fabric that will cause holes over time.

Any good Kilt Wool will resist fly away but it is in the construction of the Kilt that prevents inadvertent flashing. If the outer apron flies up there is another one underneath that is pointing the other way which will not fly up.
In the back it is the point that the pleats are stitched down than prevents too much from showing.

Now, if by lighter weights you mean less than say 12oz fabric there is nothing you can do. Those fabrics are simply too light to properly swish anyway so they are unsuitable for a good looking man's Kilt.