The double meaning of since as after and because is a well known case.
It is for instance cited by famous linguist John McWorther in "The power of Babel".
Here is the complete excerpt:
A thousand years ago, in the language
called English, since was a compound
word siththan [siððan] from the
words from after and that [sið
and ðan]1 and was only used in the
chronological "after that" sense of
- She has been sad since the day her fish died.
The because usage
- He has to have been there since they found his umbrella in the
basement
would only become established five hundred years later.
Please note that the same thing happens today with after in the news when the news media tries to avoid being liable for making unfounded accusations.
The man was arrested by the police after the purse of the victim was found in his car
Note 1: The OE words
sið and
ðan can be compared respectively to Present Day German
seit and
dann, which are often seen together in the sense of "since then" or "thereafter" but without marking causality.