What does greasy mean in Shakespearean time?

Answer 1

It means "greasy", that is, covered in grease or full of grease. Jaques in As You Like It talks about "fat and greasy citizens", "greasy" here also meaning fat or full of grease. The same is probably true of Mistress Page's description of Falstaff as a "greasy knight". More often it suggests "covered in grease" as in "greasy aprons" in Antony and Cleopatra and the greasy laundry in the Merry Wives of Windsor. Kitchen workers were prone to grease; the Syracusan Dromio says of his sister-in-law "Marry, sir, she'd the kitchen-wench, and all grease; and I know not what use to put her to but to make a lamp of her and run from her by her own light." She was fat too but this isn't what Dromio is talking about. The greasiness of kitchen wenches also shows up in "greasy Joan doth keel the pot" in Love's Labours Lost.

So, the word meant then what it means now. It had then, as it does now, the connotation of dirtiness, sleaziness, lack of class. These implications are certainly in the "greasy knight" quotation.