I am on MAster and this Steel Battleaxe (2H) kills bandits in like 3 hits over at Embershard Mine (outside of Riverwood). I picked up an Iron Battleaxe and now it takes about 5-6 hits to kill them.

Won't this level up my 2H more since I have to hit them more often?

Skill leveling is a little different in Skyrim than in MW and OB. The base damage of the weapon counts as well as the uses so you will get more use xp from the iron sword but each hit will count less than from a steel sword. So, yes, probably you will level a little faster but not that much in proportion to the increased number of hits required to make a kill.