Karen: This is also from the old marriage custom of actually tying the couple's hands together as part of the ceremony. They were not allowed to untie it until they had consummated the marriage.
Rob Flynn says: The phrase is actually 'burning the candle at both ends of the day' i.e. getting up early in the morning (and burning a candle) and going to bed late (and again burning a candle). Which is why we say that someone looking tired and haggard from overwork (or overplay) has been burning the candle at both ends...