Top-of-the-line NMC cells have energy density around 250Wh/kg at the pack level. The newer solid-state batteries can reportedly increase this to 400Wh/kg.

So a reasonable 75kWh battery pack is going to weigh around 300kg and in future around 200kg. This is... not a lot, actually. To a point where shaving off 20-30 kg from the electric motor weight is going to result in a noticeable performance/price difference.

Teslas also don't have "crazy" weight. Model 3 is 1700kg and a comparable (in size) Ford Focus is 1300kg.