So when you brew coffee, the beans are leaving behind a bit of their wonderful glorious essence. My question is how much.
What amount of coffee would you have to brew before you could see a measurable increase in mass, say 1 gram? Would this even be possible based on the evaporation during heating of the water?
It’s probably pretty close to a gram for an 8-ounce cup. Instant coffee is just brewed coffee with all the water removed and typically you use about 1 teaspoon of it for an 8-oz cup. I’d guesstimate that to weight around a gram or so.
Being a homebrewer I happen to own a hydrometer, a device that measures the specific gravity of liquids. I could brew up a few cups and measure the gravity, the only bad part is for maximum accuracy I would need to wait for it to cool to room temperature.
If I have time to do it tonight I will get back to you.
Coffee cools to room temperature whenever you answer the telephone, so try that.
My jar of Safeway brand coffee crystals has a net mass of 113 grams in a volume of 350 cubic centimeters, so its density is about 0.323 g/cc.
The directions call for one slightly rounded teaspoon per six ounce cup.
One teaspoon is 4.93cc, so call a rounded teaspoon 6 cubic centimeters.
6 X 0.323 = 1.9 grams of coffee solids per cup.
You drink that shit? What’s wrong with you? 
Of course this isn’t the same as saying that an 8 ounce cup of coffee weighs a gram more than an 8 ounce cup of water. But that is not what the poster asked, so this answer works perfectly.
I leave on the shelf, just in case of apocalypse. Probably bought it on a spin through Arco, Idaho three years ago.
If you’re worried about water loss from evaporation, I think you’ll need to be at least as worried about the loss of water stuck to the grounds.
In fact, if you’re just asking about the weight difference between ‘coffee in the cup’ and ‘water poured into the coffee maker’, the answer is going to be negative; more water sticks to the grounds (and filter) than coffee bean material is washed out.