The three weeks rule is only a rule of thumb, and a largely obsolete one at that; in the past, when good ingredients, sanitizers, and information were hard to come by, three weeks gave you plenty of time for fermentation to complete and to let off-flavors dissipate. Improved ingredients, equipment, and techniques should obviate the need for that today. In any case, it is better to use the hydrometer and bottle after the gravity has been stable for three to five days, rather than following a time schedule. There are several variables involved, and not all beers finish at the same rate; three weeks is generally the longest a moderate gravity beer will take, hence the rule of thumb.
While in the past I have followed the old rule - one week in the primary, then rack to the bright tank for two more weeks before bottling - it really isn't necessary with any ales of moderate gravity. Higher gravity ales need more aging in general, but again, you want to follow what the hydrometer says, not a time schedule.
(Lagers are a different story altogether, and inadvisable unless you have suitable temperature control and are willing to wait at least a month for cold aging.)