In this potentially final episode of Dark Souls Science, we find that the amount of stability damage dealt when kicking is related to your on-hand weapon, and it seems to be a hidden per-weapon attribute.
However, for a given weapon, the upgrade level greatly affects the amount of stability damage dealt when kicking.
The Crystal Straight Sword has the worst stability damage dealt when kicking, and the Dragonslayer Spear has by FAR the most.
The full data including screenshots and spreadsheet can be found here: http://1drv.ms/1HmPlDJ
Thanks to @voidthedark for giving the idea for this video, and @snoopyt7 for helping a LOT with the testing and editing.