As some have noted, bronze was very popular for armor and weapons until it was found that iron or steel could be stronger, lighter, and cheaper for similar use. However, if you have a power with a really robust supply of everything needed for bronze, they'd have less impetus to move toward iron/steel and would incorporate more of OTL developments in bronze. In a sense, their bronze age would last hundreds of years longer. Eventually, though, the advantages of steel would be be seen.
However, if, while in the height of their expanded bronze age, this power developed gunpowder technology (far earlier than anyone did), that combination could have a huge impact. They could easily make bronze muskets, cannon, and such. With those on the battlefield in numbers, the wisdom of developing more advanced steel armor declines -- you'd be developing platemail around the same time it's becoming obsolete. Similarly, with muskets on the battlefield before swords and such get too advanced for bronze, the need to develop greatswords and such of steel declines -- sure it's a great weapon, but not if someone's shooting at you before you can get close.