E-Mount fast zoom weight/size

You cannot directly compare the weight/size of a screw-drive A-mount lens with no built-in Image-stabilization, with an E-mount lens that has a built-in focus motor and built-in Image-stabilization (IS). In addition to that, the E-mount lens is optimized for shooting video, with the focus-drive motor optimized accordingly.

In other words, there are additional optical elements in the E-mount lens for the IS function, in addition to other things like Gyro-sensors etc. This is in addition to the motor that rings around the lens elements, making the lens FAR more bulkier than an equivalent screw-drive lens that has none of this.

As a point of comparison, the E-mount 24mm f/1.8 (with a built-in Ring motor but no IS function like the E-mount 18-200) weighs in at 225gms. The A-mount 24mm f/2 (FF lens but with smaller aperture than the E-mount lens but has a built-in motor like the E-mount lens and like the E-mount lens lacks the IS function), weighs in at 555gms (over 2 times that of the E-mount lens).