[johnday]

Technically speaking, batteries do get lighter when discharged! But not in any useful way, and entirely unlike the situation with aeroplanes, of course.

[capableweb]

Do they technically actually do get lighter? Since it's a solid-state battery, nothing is actually moving outside the battery (the ions move from one electrode to another, but they remain within the battery while charging/discharging) and because of law of conservation of mass, the weight should stay the same.

But I'm no battery expert, maybe someone knows better.

[intrasight]

E = MC^2

In special relativity, the conservation of mass does not apply if the system is open and energy escapes.