While she perceives similarities between Cloud and Zack, Aerith realizes that this isn't the natural Cloud. The lines "I'm searching for you" and "I want to meet you" are deep statements which see through to the existence of the true Cloud, which he himself isn't even aware of.
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"So you won't have a breakdown"
Aerith, appearing in Cloud's dream, tells him this to console him. From this line you can gather than Aerith has seen through to Cloud's true nature.
What Mako Daddy said.
Aeris saw that the true Cloud wasn't the Cloud who punched her in the face. Seeing through the the existence of Cloud, which is something he wasn't aware of is nothing more than SE saying: Aeris realized
something was wrong with Cloud and she saw that the true Cloud wasn't the one he was pretending to be. That's why she wanted to know that Cloud. if she already did, why the fuck would she want to meet him?
That's cause she didn't. She only knew something was wrong and Cloud wasn't Jenova's bitch. That doesn't mean she knew what or that she knew the real Cloud.
There is nothing there about Cetra powers. I'm tired of people making Aeris to be some crazy mind-reader or performer of magical feats of awesomness. She could occassionally hear the Planet, but even then it wasn't clear and she didn't always understand. She couldn't do shit. She's like Obi-Wan -- more powerful when dead
EDIT:
@ frost: No, it means she knows somethign is wrong and that there's a shell around him. Perhaps she can sense some interference (LOLZ static. Can you hear me now, Cloud?), but she doesn't know Cloud. She knows Cloud isn't Cloud, but she doesn't know who Cloud is.