I'm sure weight matters a little but torque is what gets the vehicle moving and regenerative breaking puts more back into the batteries with more weight.
Aerodynamics seem to be a more critical factor for electric vehicles. You want the vehicle to be able to cruise while using as little energy as possible, and weight doesn't matter as much for maintaining speed.
It's the same reason that most modern trains are electric or diesel-electric rather than pure diesel.
Many aircraft tow tractors are also electric these days, and they haul some fairly heavy loads.
You realize of course that regenerative braking puts more* back into the batteries for heavier vehicles only because a lot more was necessary to speed them up in the first place?
I do realize that regenerative breaking does not 100% cancel out the energy required to accelerate the vehicle.
The Model X will be ~10% heavier and Musk has stated recently that the range is expected to be ~10% less than that of the Model S.
In other words, obviously a heavier vehicle will use more power than a lighter vehicle, that's true with any fuel source, but it's a small difference in this case. They could put a battery pack with 15% more capacity in it and the range would be about the same as the Model S, but they're probably going to use the same battery as the Model S for compatibility and manufacturing reasons.
Aerodynamics seem to be a more critical factor for electric vehicles. You want the vehicle to be able to cruise while using as little energy as possible, and weight doesn't matter as much for maintaining speed.
It's the same reason that most modern trains are electric or diesel-electric rather than pure diesel.
Many aircraft tow tractors are also electric these days, and they haul some fairly heavy loads.