It's not only energy storage that has a weight problem. The last time I lifted a sizeable electric motor, it didn't exactly float free from its mountings ..
Electric motors are heavy, period... and no-one has come up with a super-lightweight electric motor yet... along with the super-lightweight battery, to go with it.
The all-electric drive system also suffers from more rapid rundown as the energy source is depleted... as many electric car users are finding, by becoming stranded, when the battery power gives out far more rapidly than they expected.
I've no doubt that electric power holds promise. The major problem is that a real breakthrough is required to advance all-electric drive systems to the point where they can become a real competitor to hydrocarbon power.
Electric cars will soon have their place in inner-city, short-trip movements... but for long distance travel by road, and for travel by air, we are still looking at hydrocarbons in the foreseeable future.
The hydrocarbons source may alter from oil to gas (coal seam or natural gas), but hydrocarbon power isn't going to be easily or rapidly displaced, certainly not within the next 20 years... peak oil or no peak oil.