You should be fine if you line them. Use a heavier blackout lining.
I made just such a pair of curtains this weekend for DGD. Although the fabric I bought was described as curtain fabric, it was more like dress fabric, it was so light, but with a blackout lining, it both excludes light and the weight of the lining makes sure that the curtains hang well.
Early Retirement - have you, would you ?
Desperately sad story of the assisted suicide of a grieving mother
