The reason for setting a tombstone at a grave is that when two people make a covenant between each other they set up a pillar as a symbol, such as the pillar that Jacob and Laban made when they established their pact, as it says in Scripture: “And Laban said to Jacob, Here is this mound and here the pillar which I have set up between you and me. This mound shall be witness and this pillar shall be witness that I am not to cross to you past this mound, and that you are not to cross to me past this mound and this pillar, with hostile intent.”
This is the sense in setting a tombstone on the grave of a deceased person. It is a symbol of the pledge between the deceased and his or her relatives. The relatives are obligated to learn Torah and give charity to commemorate and elevate the deceased’s soul, for their good deeds will always elevate the deceased’s soul from level to level, while the deceased is obliged to always appeal to God and request mercy for his or her relatives.