Cry: here's soft tissue (7)

I believe the answer is:

blubber

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'tissue' is the definition.
(I've seen this before)

'cry here's soft' is the wordplay.
'cry' becomes 'blub' (I've seen this before).
'here's soft' becomes 'ber' (I can't justify this - if you can you should give a lot more credence to this answer).
'blub'+'ber'='BLUBBER'

Can you help me to learn more?

(Other definitions for blubber that I've seen before include "Break down" , "Cry uncontrollably" , "Layer of fat under the skin of whales" , "Insulating fat" , "Weep - whale fat" .)

I've seen this clue in The Sun.

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