She took advantage of that man's weakness.

Literal

She [topic-は] that man [genitive-の] weakness [target-に] took-advantage.

つけいる (付け入る, lit. 'push in and enter') is a vivid verb for exploiting an opening — a weakness, a moment of inattention, an emotional vulnerability. The に marks what is being exploited, treating the weakness as the entry point. The verb carries a clearly negative moral tone: someone who つけいる is taking advantage in a way that wouldn't be considered honorable. It frequently shows up in business, romantic, and political contexts where one party preys on another's vulnerability.