Under what conditions does Kate agree to marry Marlow in She Stoops to Conquer?
In Act II, after her first meeting with Marlow when she appears as a gentlewoman, Kate finds Marlow's actions frankly amusing. His shyness and inability to express himself do nothing however to crush her interest in him. Note what she says:
If I could teach him a little confidence, it would be doing somebody that I know a piece of service.
This strongly suggests that Kate sets out to make Marlow more outgoing for her own benefit, so she can marry him and be happy. This is something that is supported later in Act III, when Kate and her father, Mr. Hardcastle, are talking about Marlow, and her father wants to refuse him outright because of his behaviour. Kate responds by saying she will only refuse Marlow under the following conditions:
For if you should find him less impudent, and I more presuming; if you find him more respectful, and I more importunate...
Kate therefore plans to marry Marlow only if she can make him more confident and "cure" him of his crippling shyness with her when she appears before him in her true identity as a gentlewoman of his own class. The method in which she does this is to "stoop" in terms of her own social class, disguising herself as a servingwoman, and using this disguise to bring Marlow out of his shell.