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All the Pokemon use berries or other food-based held items, e.g. Leftovers. The puzzle would involve scales and balances, maybe you need to feed a Snorlax until it can balance a scale so you can walk across it. If there's some way to involve either the Pokemon or, more ideally, the trainers getting too fat and bloated, maybe so that they tear out of their outfits in a semi-comical fashion, that would be ideal. Or maybe the puzzle is just blatantly some sort of eating contest against the Gym Leader, with magically fattening food. Whoever wins the Pokemon battle afterwards gets the weight erased.
