I wonder if it's sorta like the rocket equation. A heavier vehicle requires larger batteries to move the extra weight with a comparable range as a smaller vehicle, but the batteries are heavy too, so you need even more battery to move the heavier batteries.

It's exactly that. Battery = heavy, heavy vehicle = short range. I wonder if ICE vehicle weight is calculated with a full fuel tank? Gas / Diesel is also pretty heavy and large vehicles have large empty spaces to be filled with fuel.