How much does 1 cup of water weigh?

The density of water at 4 °C is 1 gram per milliliter (1 g/mL).

There are 236.588 mL in one cup.

So 1 cup of pure water weighs about 236.588 g (about 8.3454 ounces, avoirdupois)

This is true at 4°C (39.2 °F) where water is the densest (1000 kg/m3, and is pretty close at most other temperatures above freezing and below the boiling point of water. Water at room temperature is 998.2 kg/m3.