How can I hang small weights from a drywall ceiling in a way that's minimally destructive?
You might have answered your own question... what about a (larger) needle?

Tie the fishing wire round the middle of the needle (and perhaps use a dab of glue to hold it in place if it won't hold itself).

If you can't find a large enough needle, try a small gauge knitting needle? Again it might need a dab of glue to hold the wire in place in the centre.