I'm not a fan of the min-raise either. What does it accomplish? It's not enough to give you much fold equity. The original bettor is almost certain to call, and anyone acting after you who would call 120 is pretty likely to call 240. So, more often than not, you won't narrow the field, which is one of the goals of raising with such hands in such situations; AQ is a pretty vulnerable hand, so you're looking to get in a two-way pot with position. That means you should bet enough to discourage players after you from calling.
Also, while he doesn't know it, the opening bettor basically has pot odds to call with any two whether the third person calls the 240 or not. Giving people odds to call means your bet has a negative EV, which isn't generally a good way to play poker.
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