I doubt range is increased much by reduced weight. Only rolling resistance is reduced, but most resistance at speed is from air resistance. Since energy is reclaimed from braking, the extra mass for acceleration is balanced by the extra mass for stopping, so it doesn’t help much with stop start traffic.
It's true that it's not a huge savings, but there's some savings. The EPA estimates approximately 1% reduction in fuel economy for each 100lbs added, so you might get a few % from the the battery weight savings.
Sure, for fuel economy, presumably without regenerative braking. When you're not in smooth traffic, a whole bunch of energy is lost in braking, and that energy is directly proportional to mass.
That’s how I mentally model it anyhow.