Well, feel free to correct me on my math here, I'm no battery expert. Google says a 100 kWh battery typically weighs between 1000 and 1500 pounds. Since we'd need 6618 kWh for the hypothetical trip from Cleveland to NYC, that means we'd need 67 x 100 kWh batteries which would weigh between 67,000 and 100,000 pounds. Google also says the typical fuel load for a 737 is around 50,000 pounds, so the relative overage from batteries (since obviously you wouldn't need to carry any fuel) would be 17,000 to 50,000 pounds. This would roughly give you a passenger capacity range between 120 and nobody. Even worse if you consider the need to have some reserves of power for unexpected circumstances. There's also the problem mentioned elsewhere in this thread that the batteries don't become lighter as they're discharged, so your landing weight is the same as your takeoff weight.

So yeah, battery weight is the core problem. But if battery weight comes down by "just" 50% (and I have no idea if that's on the horizon or not) then electric aviation becomes quite viable.