Technically speaking, batteries do get lighter when discharged! But not in any useful way, and entirely unlike the situation with aeroplanes, of course.
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.
But I'm no battery expert, maybe someone knows better.