Azalea really dislikes Fairweller. She thinks of him as "a thundercloud. He never smiled. The only color he wore was black, even his waistcoat and cufflinks, giving the impression of a sleek, overlarge spider. With the added disadvantage that you couldn't squash him" (2.5). That's not a very nice description—particularly since he's fairly young and not a bad-looking guy.
Adding to his cheery appearance, he has "iron gray eyes" (2.116). Azalea thinks that his eyes are "colorless like the rest of him" (5.26) and we don't think she's just referring to his gothy wardrobe. Nope—he's utterly humorless, and almost as little fun as her dad.
But he has a good head on his shoulders (for all that he's a Whig, which is apparently the opposite political party from the royal family, another reason for them not getting along too well). He comes to take the girls out into the gardens on royal business, saying, "It is clear to me you have found one of the palace's magic passages in your room" (16.107). In other words, he's not planning to let the girls vanish down the rabbit hole or get trapped or whatever, even if he doesn't really like them.
Okay, that last part isn't entirely true. He does like one of them—Clover. And he likes her lots. He likes her enough to go up against her dad (who, let's face it, is kinda scary) in order to ask for her hand. The fact that he survives the encounter probably says more about Clover's sway with her dad than his determination, but hey, it's looking like Fairweller and Clover will have a happy ending, so good for them.