This isn't true at all, total misinformation.
I don't know about older Defenders but a modern Defender weighs 2.5 tonnes so I'd say that any ICE 4x4 is insanely heavy. There are nutters out there driving near 3 tonne Range Rovers who claim that EV's are ruining the roads because of their weight, it's utter bollocks.
A Tesla Model 3 weighs 1.7 tonnes and for comparison an Audi A3 that is full of petrol also weighs around 1.7 tonnes. At worse a Tesla Model Y EV is absolutely massive and yet only weighs 2 tonnes. That weight is better used versus an ICE 4x4 because it's all utilised in the body to carry things and people instead of carrying petrol.
Most EV's locate their batteries low and central so their centre of gravity is very low to the ground. That means that they're far more stable and maybe even impossible to roll over. And by the way, depending on the configuration a full EV battery pack can weigh the same or less than a car engine which needs a persons weight of petrol to run it...
Sorry, not having it! :)