"I placed a small stone on top his headstone"

Jewish Cemetry on Mount of Olives, Jerusalem
GNU Free Documentation LicenseJewish Cemetry on Mount of Olives, Jerusalem - Credit: Mewasul
In the Jewish religion, it is customary for a visitor to a grave to place a small stone on the headstone, using the left hand. This shows that someone visited the gravesite, and is also a way of participating in the mitzvah of burial.

In Biblical times, headstones were not used - graves were marked with mounds of stones.  Placing a stone on the pile was thus a way of maintaining and perpetuating the burial place.