This is an issue with every car, not just Barchettas, although an open car can suffer sooner.
Saggy, or non-retracting belts are caused by:
Dirty top loop.
Fluff/dirt in the reel mechanism.
Worn belt.
Retracting mechanism tired or broken.
Fixes:
Dirty top loop.
Clean with a soft damp cloth. Any cleaning material may harm the belt webbing. You do still want it to hold you in a collision.
Fluff/dirt in the reel mechanism.
Remove the belt and try to clean out all the fluff and debris around the belt reel. A paintbrush will help. It may be possible to remove the plastic covers to get at the spring inside. Clean carefully and lubricate the mechanism with a very small amount of light oil or better a silicone spray. Not WD40 it is only temporary. Too much will attract fluff.
Do not dismantle the mechanism. Your life may depend on it.
Worn belt.
If the belt edges are frayed, or getting fluffy, replace with new. Don't just trim the fluff off.
Retracting mechanism tired or broken.
Replace it.
Spraying the belt webbing with any lubricant is not recommended.
a) It may harm the webbing material long term.
b) It will get onto all your clothes, and those of your passengers. And once soaked into the webbing, you'll never get rid of it.
Have I missed anything?