Aircraft weight turns directly into fuel cost via induced-drag. If electric energy is wildly inexpensive, you can afford very heavy airframes.
1) Aircraft cost is proportional to empty weight.
2) Range is proportional to total stored energy / drag and drag is proportional to weight. If you have low specific energy, you cannot go far.
And it's true that airliners take off with more weight than they are speced to land with. They have to dump fuel if landing before burning it off.