There appears to be no product specifically designed to weigh down shower curtains. However, if you're looking for something quite heavy to attach to your shower curtain, these stainless steel tablecloth weights will be perfect. They are heavy and don't hang down too far meaning they won't drag along the floor to the extent that other versions do. As they are stainless steel, they provide a pleasant contemporary look. Most importantly, several people have reviewed these as working well on shower curtains.
In case you're wondering, these are a clip on weight. You simply pry the clip open and place the curtain edge inside. This obviously allows you to choose whether you place them on the sides, corners, or bottom of your curtain.
The weights pictured here are a four piece set, and will suit people looking to maintain a clean/modern look. Reviews also claim that these can also be used on net curtains and drapes to prevent them blowing around in the wind.
They are available on Amazon
These are quite attractive and made of hand painted resin.
Unlike other items used to add weight, these have a water/coastal theme which matches up reasonably well with bathrooms. Their actual weight is not specified, but their description states that they're heavy enough to weigh down tablecloths used outdoors in gusty conditions, so I'm assuming they will be heavy enough.
There are all sorts of different kinds available. Some look a little tacky, but I don't believe these shells would drag down the appearance of your bathroom. In fact, they could even be called a "cute accessory".
If you do decide to get something which clips onto the bottom of your curtain, remember that it may make a little 'clanking' noise if they're tapping on the sides of tubs. Although I'm assuming you could always clip them up a little higher.
These shell weights are also available on Amazon.
Please see the other posts I've written up in this blog which describe a number of other techniques and products that are available to keep your curtain from molesting you.