[hvalentim]

My voltmeter is certainly far from perfect. But that's beside the point. Even if it's not perfectly calibrated in absolute terms (although I have reasons to believe it can be accurate up to 0,1V) the matter at stake pertains a relative variation in the 7809 output provided the voltage it is supplied constantly changes (and goes up and down) very fast.

When the supplied voltage applied to my L7809CV remains consistent (for instance 12,8v) the output is also consistent at 9v give or take a couple of 0,01 of volt, which in fact can be a voltmeter issue.

For your lab test to mimic my conditions you would need to apply a constantly shifting voltage to the input, varying say 2v up and down in less than 1 second cycles.

I would suggest the L7809 has let's call it a "response time" in regulation than does not allow him to keep up at it's peak accuracy when it has to constantly adjust, the more when sometimes it's adjusting down the others up...

Otherwise, as Allan remarked, the spec.s claim no more than a "8.64 - 9.36" accuracy under 25º conditions. So it is not performing below what it claims.

EDIT: It is worth mentioning that I am testing the L7809CV in it's bare form. Adding capacitors seems to be a suggested best practice that may help a bit. I do not know/understand exactly how this is handled in WeatherDuino but it seems we have 100nf capacitors in both lines. Perhaps I need to add those two to my equation as well.

Here's an in detail illustrated article on the anatomy of these things with a number of tips:
Reverse engineering a 7805 voltage regulator