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Broadly speaking UK recipes will specify amounts by weight (lbs/ounces or metric), whereas American recipes will specify amounts by volume (cups).
Is there an explanation for how the two different approaches arose in the first place? I'm not talking about whether or not metric is used, but specifically about volume versus weight.
I'm no authority, but I have a hypothesis.
Measuring weight is more complex than measuring volume. Before the invention of the digital scale (recent history), or the spring scale (1770, by a Brit) things were weighed with a balance scale and a set of weights. Materials alone makes this more expensive than a simple cup that would hold a liquid.
Given the timing of the invention of the spring scale, and our subsequent armed revolution, and many years (decades?) of being a flat-out poor country I don't imagine that we had much money to worry about spring scales or balance scales. A cup is cheaper and simpler, and doesn't wear out or break. The durability also likely had a role to play in our journeys westward.
Likely by the time we actually could afford "fancier" methods of measurement the volume thing was just too ingrained in our heads. Plus, we tend to be stubborn (e.g. metric).
The Wikipedia answer to this is that Fannie Farmer in her 1896 very popular cookbook decided to use volume measurements for solids instead of weight measurements. In chapter 2 she explains how precise measurements are essential in following recipes and then goes on to explain how to measure flour by volume. No fanfare. My impression is that she was just codifying what was already common practice then.
So I'm voting against the traditional answer, as it does not quite explain why it became common practice. I've also read the speculation that volume measurements where common until the introduction of the metric system, which never made it to the US.
I did some more digging into this question. The Boston Cooking School helped popularize the use of volume measurements for dry ingredients. Cooking schools were part of a Domestic Science movement that was stronger in the US than in Europe. As Hobodave points out, springs scales were a British invention and it was only in the early 1900s that reliable ones started to be sold in the US. By then cups and spoons were too popular and with the government and other institutions supporting and standardizing the practice it was hard to change.
