I want heavy-lidded eyes as similar to the singer Cher as possible. Is there anything I could have done to get this?

However, a photograph is much more helpful that the written description.  Without that, we are just guessing about your concerns and how best to address them.

Creating fullness in the upper eyelid region can often be done with fillers or fat grafting.  This will help if there is hollowing in the area.  This can frequently give the desired aesthetic result.  Changing the eyelid position relative to the pupil (ptosis) would not be recommended if you have a relatively normal eyelid position now, as scarring can lead to unpredictable results, and even disruption of visual fields.