jennyema has, as usual, nailed it. It is tough to convert from volume measures to weights even if one is using only the metric or the American (actually the British Imperial) system.
One ml (metric system) of tea leaves measures considerably less than does the same volume of, oh, say lead. Just the same as a pint (American system) of lead weighs more than a pint of tea leaves.
To know how much any volume of a substance weighs one need to know the density (the weight per volume). Densities are easy to find for pure fluids, metals, and that sort of thing, but become more difficult to find when one is dealing with things like flour, sugar, and salt, substances whose individual particles can vary in size and shape, among other factors.
Things get even a bit more confusing when trying to figure out the weight of a quart (American) of something into grams (metric), because one has to solve the volume to weight conversion, and then convert between the two systems of measurements.
But many cooking problems can be handled easily.
The easiet way of course is to have both British Imperial (American) and metric volume measuring devices about (devices that measure both cups and liters), and scales that measure in both grams and ounces, as Allen did.
It gets tougher for our fellow cooks who live in other countries and may not have measuring utensils graded in cups or ounces.
Forfeit of dual measuring devices, one can make calculations.
Using the values given in:
I learned that 3.6 cups of all purpose flour weighed one pound.
That means there are just about 0.28 lbs per cup (1 divided by 3.6).
Multiply by 454 grams per lb and one gets 126 grams per cup of all purpose flour, or about 32 grams per quarter cup.
Do the same with granulated sugar at 2.3 cups per lb and one gets a value of about 49 grams per quarter cup.
There is quite a difference between the two.
For water the number comes up to about 59 grams per quarter cup.
So is sounds to me like Allen and cc's values are straight on.
Is this all a pain in the gluteus maximus, yep.
We own a number of cookbooks that use the metric system and usually just try to wing it, but then again we are both very familiar with both systems and often add what we think is about right.
Lots of luck when baking though.
Sorry I have gone on so long, but wanted to give my take on a commonly asked, and very difficult question.