Bronze is easier to forge into thin sheets. It's difficult to cast large very thin objects; these pieces of armour and shield facings were forged.

Today, we can start with rolled steel sheet (produced by a mechanised forged process, rather than hand-forged). The Greeks needed to start with a chunk of iron and forge it into a thin sheet. Slag inclusions can make it hard to do (and can weaken the final thin sheet), and the loss of iron to oxidation during forging means you lose a lot of material.

Bronze is relatively pure and uniform, so there's no problem with slag inclusions. Bronze is cold-forged, so there's no problem with trying to keep a large thin sheet at forging temperature for hot-forging. (You still need to heat the piece now and then to anneal it to relieve work-hardening, or it will crack during forging.)

So, a more expensive material, but tough, and as hard as the iron weapons it will be stopping, and without weak points due to slag inclusions when made into a thin sheet.

Note that early iron helmet bowls are usually made of multiple pieces; iron helmets with one-piece bowls are relatively recent (they become common in Europe c. AD1000, though there are some much older examples, such as this supposedly 3rd/2nd century BC Celtic helmet with a one-piece bowl), and one-piece bronze helmets are common much, much earlier.

Similarly, early metal armour with large plates is usually bronze. Where iron is used for early armour, it was usually as mail, scales, lamellae, or other small-plate constructions.

Another late use of bronze in weapons was arrowheads. Casting allowed (a) mass production of standard forms (and standard weight), and (b) easier production of complex shapes such as trilobate arrowheads. Some discussion about this in https://www.reddit.com/r/AskHistorians/comments/aexgpk/if_iron_is_really_better_than_bronze_in_every_way/