My wife and I have it pared down to what we think is the best combination:
We each have a small fanny pack, plus we carry a daypack.
Each person's pack has their own stuff (tissues, meds, sunglasses, dried fruit, ID, etc) plus a water bottle. We can spin them around to board rides, or carry them in the back where it's more comfortable. And by having one each, we keep them small and light, plus there's no "Honey, can I have..."
The daypack keeps things we want at the park, but not on our person. Jackets, change of T-shirt, camera... like that. We check it into a locker when we arrive at the park, and go back when we want it.
For instance, we may want the camera just for this parade, or that event... we go back THEN and get it, but don't carry it the rest of the time. Saves weight, don't have to worry about damage to the camera.
We also have a small soft-sided cooler (six-pack sized). We pack a couple of sodas or water apiece in their when we leave the hotel, and that gives us a cool break partway through the day. We also pack extra snacks. Snacking from out fanny packs lets US decide when and where to have meals, which saves on the $$.