Pomegranates are plants that need controlled stress to really fruit well, and what you're doing might be too comfortable for it. My grandfather had an amazing pomegranate tree in his garden, and I remember he barely watered it at all in summer once it was well established. That plant produced enormous fruit and crazy amounts of them - the secret was letting it "suffer" a bit. He only watered it during very dry spells, and this stress made the plant put all its energy into fruiting instead of vegetative growth.
Try cutting back on watering when the soil isn't completely dry, at least from June onwards. At the same time, do some serious pruning in late winter: remove the oldest branches in the center of the canopy and any suckers coming from the base, keep only the main branches well distributed. This helps air circulate better and encourages young branching that produces fruit. If the soil has been heavily fertilized with nitrogen over the past years, it could be promoting lush foliage at the expense of fruit - in that case, switch strategies next year and use a low-nitrogen fertilizer, maybe a fruit-specific one, just a couple of times in spring.
Also check the exposure: pomegranate loves direct sun as much as possible. If it's in partial shade or a less bright spot, consider moving it somewhere it gets at least 6-7 hours of sun a day. Put all of this together and you'll see the fruit start to multiply.