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It isn't really an advantage for a bad player, only a good player to be shortstacked. The bad player has to continually be lucky with that short stack to overcome playing bad, and occasionally taking winnings off the table won't overcome it in the long run. And even from the perspective of you recouping from his getting lucky on you occasionally, you only have to beat him once to get back what he took, since he won't play with a bigger stack and take even more off you by bad play. Also, when you lose to bad play, you shouldn't have the attitude that you want to get even from that specific player, but from the game as a whole, otherwise you might be led by emotion to give up your edge and play badly against him when he actually has a legitimate hand.

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I agree with everything you're saying about emotion and not trying to get it back, etc - that's really irrelevant to what I'm trying to point out. You're incorrect about short stacks not helping bad players. A good player is hurt by short stacks. A bad player is helped by it. Good players playing short stacks are denied full value for their big hands and can have too few chips to make effective advanced moves against larger foes. Bad players with short stacks have a safety net for their frequent mistakes, often get to draw for free because they're all-in and deny the good players implied odds against them.