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This is a great question. Weighing down the back of the jacket may be difficult with a sheer fabric. There are such things as “hem weights” that can be inserted into a hem, however the hem would need to be large enough for the weight to fit in (a chiffon fabric generally has a very narrow hem) and you might be able to see it through the fabric. Have you considered adding some kind of heavier edging to the jacket that might weigh it down a bit? Or even make an edging that you could hide hem weights in?
Another option to try and keep the back of the jacket down while wearing it would be to stiffen it. It would depend on what the chiffon was made from, but a polyester chiffon can take well to starch. This would only be a temporary fix and would need to be done after every washing and/or before every time it was worn, but it could work.
Related Video: How to Hem Lightweight or Sheer Fabric