Anywhere you need a small but longer lasting battery and don't care about mass. The primary issue with a larger mass is accelerating and decelerating it. However with the larger capacity, it would be less efficient but perhaps could still lead to longer range in the car if the extra energy stored overcomes the added cost of moving it around. Probably not a good thing but could be useful then in something like an electric race car or something.

Submersibles (which may not care about weight due to ballast anyhow), Batteries for Solar Storage (price dependent likely bad at first), Pacemakers, Hearing aids, once it's invented if robotics outpace man engineered human biology, maybe smart blood.

Perhaps also Nanobots, Active 3d Glasses, Cell phones, Laptops, Tablets, Smart Watches that go for smaller space vs weight.

Outside of that perhaps home appliances like a portable bread machine, or a hand-held wireless electric apple peeler, very small things like a rock that has a hidden microphone / camera in it for spycraft, perhaps a heated travel mug to keep your cider warm, or an electric bowl for keeping great-gravy from coagulating on the dining room table, maybe a warm pie plate because who doesn't like warm cherry pie? Perhaps some sort of autonomous mud tunneling microbots, rather have a large boring machine just let these small guys go and be patient and in a decade or two you'll have your tunnel, electric candles in churches could cut down on unnecessary wax use, and helmet lamps used for stuff like lead mining could also find a use (added neck strain not withstanding). Not sure if the added weight would be too much for a target-practice duck that swam around in a lake or not, but if not, that might be the right answer.