This in fact is not a spoken word so much as a sound. It is the same sound made when someone is sniffing their nose as they are crying or trying to stop crying. The recovery sniffs is the sound you are mocking.

It is a sarcastic way to show someone you feel no pity for their situation.

Just like playing the tiny violin for a person, this mocks the persons sadness by "crying" along with them. See example
Bjorn: Yesterday, my girlfriend told me that my clothing is out of style and it really hurt my feelings.

Bennett: (very sarcastic)"Sniff-Sniff".... "Sniff- Sniff" oooh "sniff-sniff"...that's just terrible

Bjorn: Oh shut up
by Randoni April 6, 2009
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refers to powder cocaine only, not crack
"Do you know where to get any sniff sniff?"
by KSU Grad November 9, 2007
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