This dramatically depends on the cars you’re comparing, a Tesla Model 3 is going to be lighter than a Range Rover Defender but a like for like comparison between an electric car and a petrol car of the same exterior size/shape and of a similar performance etc should show the electric car always being slightly heavier (the batteries are pretty heavy), however, there are always going to be heavier cars, vans or trucks out there on the roads and whilst all vehicles cause damage over time it’s going to only ever be marginal compared with large trucks with trailers etc.
Example weight difference:
Hyundai Kona Electric 64kWh = 1685 kg
Hyundai Kona Petrol = 1208 kg
Tesla Model 3 = 1,726 kg
Land Rover Defender = 2133 kg