Why does Allah punish the person in the grave for the wailing done by his relatives, since one soul does not bear the sin of another?

The Muslim should request for his family not to wail, etc and include this request in their wasiya (will and testament). If the family members still carry on with wailing, etc, then he is no longer responsible and will not be punished. If he does not include this request in his wasiya, he will be responsible because they are doing this because of him, and he did not try to prevent them. Normally it is women who do this.

AND ALLAH KNOWS BEST

Shaykh Ibrahim Dremali