Chip Leader, purposely keeping low stack in game.

This is a hypothetical. Let me know your thoughts on it.
Say there are 3 or 4 people left, and you are a big chip leader, 2X the guy in second. Top 3 get money.

You are currently in a hand with the smallest chip stack who has raised everything he has except 30 chips. You look down (or at your screen) and find AA.

What should you do?
Let's say you decide to call rather than raise, and I'll get to my reasoning in a sec.
To your surprise A - A - 7 comes down, and you have flopped the nuts.
What should you do now? You have 4000 chips, and he has 30 remaining.

I think you should check it down and let him keep his 30 chips.

This way, on the next hand, when it is the 2nd lowest stack's big blind, you can raise him and he will be threatened to lose all his money and not place in the money , or not place as high.

Is this a really simple strategy? Does everyone do this?
Is there a counter argument to this play?

-MG