* She's a refined Southern Belle (or so she claims): Stanley sees Blanche's elaborate manners and flowery language as pretentious affectations, masking something less than respectable. He's suspicious of her aristocratic airs, viewing them as a contrast to his own working-class values.
* She's fallen on hard times: He learns, or suspects, that Blanche has lost her Belle Reve plantation and is financially destitute, forcing her to rely on Stella's kindness. This fuels his suspicion that she's not as virtuous as she presents herself.
* She's seeking refuge (and perhaps something else): He realizes Blanche has come to New Orleans to escape something, and he suspects it's related to her past behavior. He interprets her dependence on Stella as manipulative.
* Rumors of her past: Stanley picks up snippets of gossip, and through his own sharp observation, he suspects Blanche's promiscuity and the reasons for her expulsion from Laurel. He doesn't have all the details, but he understands enough to use the information to destroy her. He actively seeks out and interprets information that confirms his suspicions. His understanding is often skewed by his own prejudices.
Stanley's knowledge of Blanche is a combination of fact, speculation, and deliberate manipulation. He doesn't possess complete knowledge, but he cleverly uses what he *does* know—and what he *suspects*—to dismantle Blanche's façade and ultimately to destroy her. His "knowledge" is instrumental in his systematic undermining of Blanche's position and reputation.