I want to know - given no increase in activity - how long does it take
for an additional 300 calories to show up on the scales in terms of
fat body weight? In other words, if I eat a piece of cheesecake, will
it take more than 12 hours to show up as fat?, 24 hours?  Do we know?

My brief search failed to turn up references on the amount of time it
takes to turn excess calories into body fat. Other GA Researchers may
find it useful to know that this process is called "de novo
lipogenesis."

On average, you need to consume 3,500 calories above your requirements
to put on a pound in weight. A surplus 300 calories will add
approximately 1.3 ounces to your weight, therefore, it will not show
up on typical bathroom scales.

A gram of fat is equivalent to 9 calories (gives the same calculations
as tehuti-ga).

There are many other factors which may impact whether the ingestion of
an extra 300 calories is actually turned into extra weight, however
(such as absorbtion, metabolic activity - which is not completely tied
to activity - brown fat burns calories futilely, ie. without storing
them, and thus may "use up" calories without any weight gain).

In short, there probably is no simple answer to your question as it
will be dependent upon many factors which are not easily measureable. 
Sorry for not having a good answer for you.

synarchy