Now that everyone's certain it's because, I would venture to say that you would use "so" similar to the way that you would use "then". It shows that your actions or feelings were following by actions.
It was cold outside, so I put on my sweater.
I put on my sweater because it was cold outside.
I went outside and then I put on my sweater.
That's what it seems like, but I could be wrong as I didn't take it from a book or anything.
Its definitely BECAUSE. It implies that is the reason why you went to bed. If you use SO, it implies the reason you were tired was because you went to bed, which doesnt makes sense. :lol: