Cry buckets -- thick tissue! (7)

I believe the answer is:

blubber

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

'cry buckets thick' is the wordplay.
'cry' becomes 'blub' (I've seen this before).
'buckets thick' becomes 'ber' (I am not sure about this - if you are sure 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 "Fatty tissue of a whale" , "Sob loudly" , "Fat of sea mammals - cry" , "source of oil" , "Layer of fat under the skin of whales" .)

I've seen this clue in The Telegraph.

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