Most of them are under 2m in width. The average weight of an EV is 1940kg with only 7 models below 1500kg. Part of the reason for that is that batteries are between 500kg and 1200kg (depending on battery size). The arbitrary 2000kg limit for EVs thus cuts out about a third of all EVs. Whereas if you apply that to ICE cars you are only cutting out a tiny amount of the market (usually the top end luxury cars).
Whilst there are technical reasons for EVs to be heavier, there are also perverse incentives; many (most?) new EVs will be company cars, and AIUI the BIK system effectively gives no ceiling to a very big tax break for expensive EVs.
So many EVs are luxury heavy models because you get nearly 40% off them through the tax system. Remove that, and I'd wager that EV sizes and weights would come down significantly.
[caveat: it's entirely possible I've misunderstood the tax system]