They don't - they measure by ratio. 1 cup originally meant just that - whatever cup you had lying around. in an era in the late 19C when few had access to expensive scales, the idea of one level cup became a simple antidote to "butter the size of an egg" recipies. Fannie Farmer's book in 1896 popularised standard ratio measures - see an episode of QI for this and related jokes :-)

Except the sometimes come with units that aren't relative, such as "one egg" or "one teaspoon of sugar".

It's quicker sometimes.

This morning I made some oatmeal. I took a 1/2 measuring cup, scooped out some oatmeal, shook it quickly to remove the overflow, threw it in a pot, and dropped the measuring cup in my sink. It took around 5-10 seconds.

If I had to do the same by weight, I would have had to get my scale, put on a bowl, zero the scale, slowly start pouring oatmeal onto the scale until it reached the desired weight, throw that into a pot, put the bowl in my sink, and put the scale away. That'll probably run around 15-20 seconds. If I screw up and poured too much into the bowl by accident, it'll take a lot longer to correct than briefly shaking a pre-sized 1/2 measuring cup.

Other times a scale is much easier to use too; it just depends on the context.

You would put the pot directly on the scale, surely. No need for an intermediate container.

You'd put a pot of boiling water on a scale? Wouldn't that risk damaging it?

I don't make oatmeal, so I don't know the exact procedure, but if one is bring the water to a boil before putting in the oats, then the simple solution is just to use your serving bowl — the one you will eat the cooked meal from — instead. I do that with pasta, for example.

The extra 10 seconds are an acceptable cost when it comes to trying to figure out how add 3/4 of a cup of margarine.

I hate measuring anything by volume. Life seems much easier if you just treat every liquid as 1g per ml and only ever use scales.

Also in regards to accuracy, weight never changes.

Volume fluctuates depending on temperature.

Weight does change around the world, mostly because at the equator you are farther away from the centre of mass of the earth than you are at the poles, but also because of local gravity anomalies. It's mass that never changes, so maybe we should all get an inertial balance for our kitchen!

Unless you are measuring ethanol, which is more like 0.78g per mL.

So his method comes with additional health benefits for free.