The maths doesn't work like that. Weight is actually not a huge factor in cycling performance because you mostly go horizontally. Top athletes only go for super-light bikes because they need every tiny advantage they can get.
Adding a battery will increase the weight a bit, but the extra power from the battery more than makes up for it. Let's do some massively oversimplified maths:
A lithium ion battery might have an energy density of 0.5 MJ/kg. A typical insane Tour de France climb might be 2000m. To lift itself that high, the battery-motor system needs to only be (20009.81/500000) ~= 4% efficient!
The actual efficiency will be a lot* higher than that. Usually over 50%, so adding a battery is definitely worth it.
(I haven't mentioned the weight of the motor, which is usually more than the battery - at least on conventional e-bikes, but it still works out as being definitely worth adding.)
Adding a battery will increase the weight a bit, but the extra power from the battery more than makes up for it. Let's do some massively oversimplified maths:
A lithium ion battery might have an energy density of 0.5 MJ/kg. A typical insane Tour de France climb might be 2000m. To lift itself that high, the battery-motor system needs to only be (20009.81/500000) ~= 4% efficient!
The actual efficiency will be a lot* higher than that. Usually over 50%, so adding a battery is definitely worth it.
(I haven't mentioned the weight of the motor, which is usually more than the battery - at least on conventional e-bikes, but it still works out as being definitely worth adding.)