In accordance with the time and the culture, William is courting Kit. His unspoken intentions are not immediately known to Kit. Judith has to explain them to her. When he mentions the work on his house, he is letting Kit know that he will soon be asking her uncle for his blessing in their marriage. He is building a fine house for himself and his future life. All of the time that he spends with Kit shows that she is the one he intends to marry.
William calls on Kit many times, starting in Chapter 7. The visits are always pretty uncomfortable for Kit, because they seem to have nothing to talk about and he seems content to just sit. She doesn't know what is expected of her, and their time together is stiff, literally so in William's case. (Look at how he sits.)
When they do talk, William will sometimes drop deeply meaningful thoughts or observations into the conversation that indicate his future plans, but Kit misses their meaning a lot of the time, and the others, especially Judith, must interpret.