They weigh nothing wrapped up in silk! (5)
I believe the answer is:
kilos
'they weigh' is the definition.
The definition suggests an adverb but the answer is not.
'nothing wrapped up in silk' is the wordplay.
'nothing' becomes 'O' (looks like zero - 0).
'wrapped' indicates putting letters inside.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'in silk' becomes 'slik' (I can't explain this - if you can you should give a lot more credence to this answer).
'slik' in reverse letter order is 'kils'.
'o' put within 'kils' is 'KILOS'.
Can you help me to learn more?
(Other definitions for kilos that I've seen before include "Metric weights" , "Units of weight of 1000 grams" , "Units of mass" , "Units of weight in metric system" .)