How much moisture does an average human body lose (per hour/day/minute/whatever) through respiration? Do we lose body fluid just by breathing?

Rates can vary by a wide range, depending on exertion and outside conditions (temperature and humidity). The article I quote below gives from 7 to 70 milliliters (grams) per hour.

The body also creates water in cellular respiration, however since glucose is oxidized to CO2 and H2O. A typical breath is 0.5 liters of air, of which 4% is used. (The remaining oxygen is exhaled). So we're talking ~20 mg of oxygen per breath, about 300mg per minute or 18 grams per hour. Some further chemical calculations show that this combines with 32 grams of glucose to form 30 grams of CO2 and 20 grams of H2O.

You're thus about breaking even - the amount you breathe out is around the amount you gain from breathing oxygen and using it.

https://pubmed.ncbi.nlm.nih.gov/22714078/