Unfortunately that was bad play. With AQ suited, especially 4-handed, you want to raise at least 3 times the big blind, not just minraise. You want to raise even bigger when against loose players, because they will call with a HUGE range of hands for anything up to 3xBB. Since there was only 1 loose player and 2 tight players, you would want to raise to 800 or 1000 (4 or 5 times BB). If either of the tight players call, you know they have something strong enough for them to want to play it post-flop. A loose agressive player often will fold to a big pre-flop raise if they don't have at least a good hand because they like to be the agressor of the hand, not the caller.
Your preflop minraise gave seat 3 4-to-1 pot odds to call (he has to call 200 into a pot of 800), and only an idiot would fold to that when he originally limped in under the gun. So then the small blind has 5-to-1 odds to call (200 into a now 1000 pot), again, very profitable to call. With 3 players in the pot and the loose agressive player having position over you, AQ becomes a lot weaker, because now you have no idea what he has and you have to guess whether he hit anything or not.
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