Kit matures in several ways. When she first arrives at the Tyler’s home, she has has no experience with hard work. In Barbados, her servant girl was the one who worked. Kit learns to contribute to the difficult and lengthy work of each day. She diligently works to improve skills that her cousins already do well. She learns to accept the austere life of a farming family. It isn’t until she sets aside her own needs to care for her family during their time of illness that her efforts are acknowledged.
Another way that she matures is in her ability to appreciate the beauty in the world around her, even though it is different than that of her beloved island home. As the seasons changed in her New England home, she is awed by the natural wonders that she sees.
Finally, her most important change is when she is able to look inside herself and realize that she has feelings for Nat. Their relationship develops throughout the story and is not always smooth. At the end of the book, they both realize they are in love and are able to communicate that directly to each other.
In a word, markedly. However, some of her changes are not due to maturity, but due to finding ways to fit in and people who love her (Hannah, Nat, Prudence).
The main ways you can see her maturity is the way she declines William's proposal and the new respect she has for her uncle. Early in the book she would have been harsher with William and failed to understand her uncle.