At one point, I worked out that US dimes, quarters, and half dollars all weigh $20/lb (iirc), which made the task of counting my accumulated change a lot easier.
https://en.wikipedia.org/wiki/Coins_of_the_United_States_dol... confirms that, and shows it works for dollar coins, too (I’m using the weights in grains because that makes the comparison easier; a pound is exactly 7,000 grains)
Dime: 35 gr
Quarter: 87.5 gr
Half-dollar: 175 gr
Dollar: 350 gr
Nickel is ~5 grams. Dollar bill is ~1 gram.