[kgs]

This is largely an academic question, but it's one I've pondered without points for comparison.

I exclusively keg in 3 and 2.5 gallon kegs, and I "set and forget" the kegs and typically only tap them on weekends, so I'm not really sure at what point they become ready.

It seems logical to me that at the same temp and PSI small kegs would carb up faster (a quantity of gas is being absorbed into a quantity of liquid at a set rate) but it wouldn't be the first time I learned new "beer math." I see a lot of reports of "ten days" for carbing and my hunch is it's more like 7 days or less for me, but there are a lot of variables to consider, including the meaning of "ready." 

I am also curious about the variables of head spaces and wort gravity.

I'm also guessing that two small kegs on the same manifold and regulator will carb at the same rate.

[mabrungard]

Carbonation can be virtually instantaneous, as witnessed at any soda fountain. However, that produces big, coarse bubbles. Fine carbonation is the result of hydration of carbon dioxide and that chemical process is time- and temperature-dependent. For those of us that put the keg into the cooler and put the gas on, its going to take a couple of weeks for the reaction process to complete. I suppose that we could speed the process by keeping the keg warmer while on the gas, but that might not be ideal for some brewers.

I don't believe that there would be a difference in achieving fine carbonation in smaller or larger kegs.

[goose]

Also the rate of absorption of CO2 is lower the warmer the beer is.

[RC]

Your logic is correct. Think of carbonation in terms of the number of CO2 molecules dissolved in the beer. For half the volume of beer (e.g. 3 gal), you will need half the number of CO2 molecules to achieve the same level of carbonation as the full volume (e.g. 6 gal).

If you're force-carbing your beers and you normally set your regulator to ~9psi (at low-30s temp), it's safe to give it half the carb time of a ~6 gal batch, i.e. 5-7 days, to achieve a "typical" carbonation (~2.5 vol). Or you could crank the pressure to ~20psi and give it half the time.

I normally burst-carb ~4.75gal using 40psi for 24 hrs. This gets me to 2.2-2.3 vol, which is drinkable (and enjoyable!) regardless of the style. But then I crank the psi down and "fine-tune" the carbonation as needed to achieve the desired vols of CO2.

Gravity makes no appreciable difference in carb rate. Headspace does. The more headspace, the faster the carbonation. If you have your regulator set to more than what's required to achieve your desired vols, you'll over-carb if you leave it too long, so watch out for that.