How do the Woods know that William Ashby is serious about courting Kit?

One day, William Ashby pays a social call to the Wood residence. Naturally, Kit is there too. During a heated political discussion, Kit becomes impressed by how intelligent William is and how he stands up to her uncle Matthew. Having said that, he's still rather shy in Kit's presence. After William leaves, Kit expresses the opinion that he won't return. Her cousin Judith doesn't agree. Why? Well, William is in the process of building a house, and as Judith explains, William said years before that he'd only start building a house once he'd made his mind up that he was going to look for a wife.
Kit is horrified at the realization that William is paying court to her. There's not exactly much chemistry between them; they barely exchanged a word when he came over to the house. Aunt Rachel confirms that William is indeed serious about courting Kit. However, she reassures her niece that although Kit and William may seem like strangers now, in due course she's sure they'll have plenty to talk about.