That weight constraint cuts both ways though, right? An electric plane charged for a 500 mile flight weighs the same as one charged for a 2000 mile flight, and the max landing weight of (e.g.) a 737 is substantially lower than the max takeoff weight. That means the maximum passenger load of the electric plane can never be as high as one fuelled by an energy source that leaves the plane over the course of the flight. So yes it's more efficient in terms of direct energy use, but it's less efficient in terms of the ratio of work done moving the passengers to work done moving the vehicle, first because you can't stuff as many on, and second because the mass of the vehicle itself doesn't drop over time.

EDIT: unless, of course, you have removable batteries that let you carry less weight for a shorter flight. That might be the only way to make this practical, and would have some other benefits: you could charge them off-site, for instance. It creates a hell of a logistics problem, but no bigger than liquid fuel.