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Signs for PITY
Meaning: the feeling of sorrow and compassion caused by the suffering and misfortunes of others; also pitiful.
Q: "Is there any difference when one would use single hand vs double hands?"
Yes, to some degree. It's not possible to give a black and white answer for subtly various contexts. But, generally, the first one can be used in informal register or used as a casual meaning. The double-handed sign may be used with some degree of emphasis or used in formal register. In some other cases, either of them may be used without much difference.
In addition, when one signs with larger and longer or slightly slower movement with the "oo" mouth morpheme, it means VERY-PITY or VERY-PITIFUL.
Related signs: sorry for, SYMPATHY, COMPASSION, MERCY.
Deaf Culture and tidbits
Deaf people generally don't embrace a paternalistic attitude. We don't need a pity (except for a speed ticket, kidding). We appreciate accessibility and equality (equity).
"Do/Don't" learning moment for a hearing person in real life: The hearing person (waitress) should have asked the Deaf man directly by writing instead of asking the child a question.