Why do we say, "keep a stiff upper lip"?

I've never understood the origin of the phrase, "keep a stiff upper lip". Presumably it's something to do with avoiding crying (as it means to remain stoical), but if anything it's the bottom lip that may wobble before one cries; generally the upper lip always stays stiff anyway. So, why do we say this to indicate stoicism?

As reported from the Online Etymology Dictionary, keep a stiff upper lip is attested from 1815.
It is probably referring to the facial mimic, in the same way bite one's lip and curl one's lip do.

The meaning of a stiff upper lip reported by the NOAD is "a quality of uncomplaining stoicism."

Senior managers had to keep a stiff upper lip and remain.

From the Phrase Finder:

Remain resolute and unemotional in the face of adversity, or even tragedy.

This is such a clichéd expression that it is difficult to imagine doing anything else with a stiff upper lip apart from keeping it. It is similar to 'keep a straight face'

Hope that explained why we use it.