Bronze is too often being heavier than iron because their main component, copper is heavier than Iron. While tin is lighter, too much tin made bronze too soft for proper protection. The Greek Bronze armor is actually quite heavy, being 95% copper with 5% tin at the average.
Weight problem aside, Bronze only give marginally better protection from stabbing weapons compared to their contemporary linothorax when someone consider the practically far cheaper cost required for linen sheets and animal glue. Sure, Bronze cuirass would fare much better against slashes, but then the most common weapons is neither sword nor axe but spear.
The advantage against slashes also quickly negated when you consider historical reinforced linothorax, that is reinforcex by bronze scales. That's right, Bronze-scale Linothorax gave best of Linothorax and Bronze armor while being cheaper than the later. Guess why Bronze is most often used as scales now?