It is currently a Jewish custom to put a pebble on the headstone when one visits a grave to mark that you have been there and that you respect the one who has passed on.
It is difficult to know exactly when and why the custom originated and whether it is strictly Jewish. I personally suspect that this custom arose out of the time (possible Roman or earlier) when people - not all Jews - would weigh down the grave or seal the tomb with a stone in order to: (1) prevent anyone including animals from harming the body and (2) prevent an evil spirit from escaping out to harm us.
Best Wishes,
Rabbi Barry Dov Lerner
