So there's the yeast thing for sure (less of 'em, takes a while to metabolize, etc)
There's also the physical carbing process - actually dissolving a liquid into a gas. At higher pressure it works faster. At lower pressures (i.e., that which bottles can handle) it takes longer. So even if you have positive pressure after a week, it still isn't properly carbed because the CO2 isn't fully dissolved yet.
A lot of guys that taste early notice it tastes harsh & fizzy - that's because the CO2 isn't fully dissolved and comes out of solution easier - carbonic acid on your tongue, no fun. But over time, the bubbles get smaller & less harsh tasting. Hence the 3 week timeline.
I posted this on passedpawn's other thread but I'll paste it here. My understanding is that the above is not true at all.
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It seems that quite a few people think that a yeast-initiated carbonation in the bottle causes the headspace to pressurize with more CO2 molecules than are initially dissolved in the beer from the metabolism of the sugars. I think this is an issue of mixing concepts we learn from the application of external CO2 in a force carbonation situation.
First, keep in mind that in a closed system of liquid and co2, the concentration of CO2 will always seek equilibrium. The transfer from an area of higher concentration to lower is a result of diffusion. Yes, I do agree that the process can take a little time (dependent on a couple different factors).
In a force carb situation, the concentration of CO2 in the beer is generally low (it depends on what temperature the beer was fermented at as well as what temperature it was subsequently warmed to while still in an open container (airlocks count since gas can escape).
Think of it this way: The beer is essentially generating CO2 in the carboy and it has to push against the ambient atmosphere to escape through the airlock. At sea level, that's about 14psi. If you fermented the beer at a rock solid 70F, when fermentation is done, the dissolved CO2 is approximately .7 volumes before you do anything else. In other words, as it was fermenting, the beer AND the headspace were sitting at 14psi or 1ATM and .7 volumes of CO2 cannot escape from the beer. In reality, the concentration in the beer will be a bit higher than the headspace because it's actively being generated and that's why a bubble forms and rises to the surface. When fermentation is over, eventually all the excess CO2 in the beer will equalized to the headspace resulting in .7 volumes dissolved.
Now you take that beer, transfer it to a bottle, add sugar, and seal the cap. Now the ambient 1ATM of pressure is irrelevant. We're in a closed system. As yeast metabolize the sugar and create CO2, the concentration of CO2 in the beer is immediately higher than that of the headspace, let's say .8 volumes... diffusion is about to make the headpace equal and so on. In no way would the headspace ever have a higher concentration of CO2 than the beer in which it originated. The yeast don't swim to the surface to fart.
One last side note that isn't really on topic, but perhaps interesting anyway. If you have a beer in a carboy that is done actively fermenting, the CO2 concentration in the beer and in the headspace will eventually equilibrate to the concentration of CO2 in the area it's sitting in. For all intents and purposes, it's the concentration of earth's atmosphere (.0387% by volume). This sort of blows people's minds because you think, how can CO2 get past the water in the airlock? It diffuses into the water, then it diffuses out on the other side. Oxygen and nitrogen do the same thing in the opposite direction. The water just slows it down.
