Electric vehicles are often heavier than comparable ICE vehicles, but not necessarily larger or even large. Chevy Bolt, VW ID.4, Smart Fortwo EQ etc are all perfectly small electric vehicles.
Batteries tend to take up the bottom couple inches of the car, as the "skateboard" design wins. 2170 cells are 70mm tall, 2.75 inches. That's not a huge factor. Also, it doesn't affect the incredibly crucial hood height, which could be greatly lowered since there's no engine/engine bay needed! Also the underside of gas cars need at least exhaust, sometimes drive axles, and usually other crap that can be deleted from ev's that helps lower EVs too. I don't think EVs are practically any taller.
They also, recently, have all the weight at the bottom, which is extremely from a handling/stability perspective. Even if you slam on the breaks, sideways at speed, you ain't gonna flip (some SUV's excepted). This is useful for emergency braking.
As for weight, the main potential problem is braking. Thankfully anti-lock brakes & big calipers are quite amazing. Ioniq vehicles have a 60-0 stopping distance of 118ft, which is on the low end of most vehicles in general, such as the also well performing Honda Accord Sport 2.0T. In car on car situations the additional weight has extra inertia but cars are generally quite resillient. As for pedestrians bicyclists & others light targets, cars already weighed so vastly much more that it's hard to imagine the extra weight changing 99.999% of accident outcomes significantly.
