No, a charged battery is not heavier than a depleted one. The weight of a battery is determined by the mass of its components, such as the electrodes, electrolyte, and casing. The charging or discharging process of a battery involves the movement of electrons between these components, but it does not change the overall mass of the battery.
The energy stored in a battery is in the form of chemical potential energy, which is converted into electrical energy during discharge. When a battery is charged, this process is reversed, and electrical energy is converted back into chemical potential energy. However, these energy conversions do not result in any significant change in the mass of the battery.
It's worth noting that certain types of batteries, such as rechargeable lithium-ion batteries, may undergo small changes in weight due to the absorption or release of small amounts of gases during charging and discharging. However, these changes are generally negligible and would not significantly affect the overall weight of the battery.