My general recommendation is to let your draper decide what kind of weight is right. If you are sewing yourself, casual cafe curtains or unlined draperies need not be weighted. If you are making substantial draperies, you are probably pretty skilled and have your own opinion for will do what works best for your fabric and construction!
Adding a bit of metal to the edge of fabrics is a very, very old technique. Heavy chain is added to theatrical curtains to help them fall properly - often so heavy that it is often inserted in to a canvas pocket and not directly to the drapery hem which it might tear. A heavy rod or “crash bar” is crucial to the working of a Roman shade, helping it drop easily and keeping it flat.
Weights are often added to very structured clothing, like men’s jackets, or to hems to keep them stable. Most of you know about the weights or chain that are sewn in to Queen Elizabeth's hems so that her skirts NEVER blow up, no matter how rough the winds. Coco Chanel famously sewed chain in to the hems of her classic jackets to make them hang properly and there is a wonderful discussion of this on the Courtauld Institute blog.
Still, I am a bit on the fence about weights in curtains. Mostly, I feel that simple unlined curtains should not be weighted. They are meant to flutter around in the breeze a bit. If the curtains are more than a fabric width wide or rather long, then weights can help the training process of getting those nice vertical folds and can help in places like the seams and vertical hems where the fabric may pull up a bit.
Otherwise I would leave the weights out. Linen particularly can stretch and a lighter weight linen (like handky weight) can end up longer at the weighted corners.
Weights come in singles, so to speak, and chain. They are lead and nowadays encased in vinyl or cord. Properly (and in the old days for fine sewing) they should be in muslin. Sometimes on line you see someone showing an old weight and wondering if it’s a weird kind of button. They should never however be on the exterior of a textile. They are LEAD after all.
Note: It’s possible to use other materials (like quarters or pennies) but they really don’t have the weight to be useful in my opinion.
I prefer individual weights to the chain. The modern lead chain is not very heavy and it can make a little lump or ridge at the hem. In this case, you may use chain of another material besides lead although it will probably have to be bulkier. For more substantial or interlined drapes this is not a problem.