Was the relationship between Marlow and Kate based on love or just liking in She Stoops to Conquer?
It is clear from Act V that Marlow is definitely in love with Kate. Note what he says when he declares his love for her, when she is still disguised as a servingmaid:
But every moment that I converse with you, steals in some new grace, heightens the picture, and gives it stronger expression. What at first seemed rustic plainness, now appears refined simplicity. What seemed forward assurance, now strikes me as the result of courageous innocence, and conscious virtue.
What is key to realise is that Marlow here in this quote states very obviously that he is not only interested in Kate's beauty, but it is more and more her character that attracts her to him. The fact that he is willing to risk the displeasure of his father by marrying a servingmaid clearly indicates that he is in love with Kate, and that this love is genuine.
Admittedly, it is harder to tell from what Kate says about Marlow whether she too is genuinely in love. It is in Act IV after Marlow, apparently overcome by his feelings towards Kate, leaves because he recognises if he doesn't he might do or say something he might regret, that Kate shows her true feelings:
I never knew half his merit till now. He shall not go, if I have power or art to detain him.
This clearly shows a determination to marry Marlow and to keep him for herself, and perhaps we are able to infer that this is because of a genuine love that is springing forth from having seen Marlow's true character. This is the only indication that play gives, however, of her true feelings as about Marlow. Perhaps what is more interesting to consider is whether the play shows that these two characters would make a suitable marriage in the long run, which I believe it does.