The Z8’s advantage is easiest to see on days when you do not need a vertical grip. Its body weighs about 820 g, compared with about 1160 g for the Z9. Those are body-only figures, excluding batteries, cards and lenses. The Z9’s integrated vertical grip is always part of what you carry; the Z8 can stay smaller until a job calls for its optional MB-N12 grip.
For frequent portrait-orientation shooting, the Z9 gives you vertical controls without attaching an accessory. It uses the EN-EL18d battery, while the Z8 uses the EN-EL15c; the two battery families are not interchangeable. The Z9’s standard battery has more rated energy than a single standard Z8 battery. That is a practical reason to accept the larger body for long sessions, though it does not specify how many hours your shooting will last. Use, temperature and battery condition still determine endurance.
The Z8 has a middle path. Adding the MB-N12 supplies vertical controls and room for two EN-EL15c batteries in total; it replaces the battery inside the camera, so the setup does not hold three. The grip adds bulk and weight, but can come off again when you want the lighter body. This makes it useful when long sessions or vertical shooting are occasional rather than the reason for every outing.
Once the Z8 is fitted with the grip and batteries, its bare-body weight no longer describes what you carry. The smaller body is most useful when you can leave the accessory off for a meaningful part of your shooting. If vertical controls and the larger single battery are needed on nearly every job, the Z9’s permanent size has a clearer purpose.