Cape, one with lead weights in sash (5)

I believe the answer is:
amice
This clue might be a double definition.
'cape' is the first definition.
Both the definition and answer are singular nouns.
Perhaps there's a link between them I don't understand?
'one with lead weights in sash' is the second definition.
I can't judge whether this definition defines the answer.
Can you help me to learn more?
(Other definitions for amice that I've seen before include "hood" , "Linen rectangle worn by priests" , "priestly garment?" , "Priest's garment" , "church vestment" .)
