Old woman, ultimately rather frivolous, chewing minute sweet (11)

I believe the answer is:

marshmallow

'sweet' is the definition.
(marshmallow is a kind of sweet)

I don't understand the remainder of the clue.

(Other definitions for marshmallow that I've seen before include "Confection commonly toasted" , "Spongy jellylike sweet" , "Sweet, often toasted" , "sweet little thing" , "Spongy confection - pink-flowering plant" .)

I've seen this clue in The Times.

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