The Prioress is trying to be very, well, dainty. She has all these funny habits, like singing through her nose, speaking incorrect French, and eating so carefully that she never spills a drop. She does these things, Chaucer tells us, because she "peyned hir to countrefete cheere / of court" (139 – 140), or tries very hard to seem courtly. When she sees a mouse caught in a trap, she weeps, perhaps believing that this is how a damsel of the court would behave. Of course, two lines later, we learn that she has no problem feeding her hounds flesh, so her weeping over the trapped mouse is probably, like most of her habits, an affectation – a behavior the Prioress adopts to seem a certain way (in this case, like a courtly damsel), but which doesn't really reveal her true feelings.
