Why do Jews put stones on grave markers?

My guess, they are cheap, almost universally available, and (here's the actual Jewish angle) incapable of accepting ritual impurity (tumah).  They are inherently pure, from a Jewish legal/religious (halachic) perspective, and thus perfect for placing on the memorial of those of whom we say, zichrono,ah livracha, may his/her memory be a blessing, referring I think to those Biblical figures of whom H" said, all the peoples will be blessed in you.


Another thought:  Many cultures put some of their native soil in or on a grave in a foreign country.  This could be a vestigial version of that.