As I recall, it was a time-span that was decided upon that wasn't too short so, as Karr said, people wouldn't be respawning over and over for whatever reason (reputation, force testing, etc) but not too long as to be absurdly long.
The 3 week wait is, primarily, looking ahead to combat. It's so that you can't die, respawn at your faction's HQ, get in a new ship, and dive straight into the fight. There are additional factors, but this is the oldest explanation I've heard.
Death is a penalty, in this game, and the 3 week wait is designed to reflect that, making it undesirable and so that a new character is more of a fresh start.
Why 3, and not 2 or 4? *shrugs* It's a slightly arbitrary number, but presumably 3 is thought to be not too long so people quit, but long enough to fulfill the mentioned requirements.