Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Witty, Sarcastic, Affectionate
The narrator admits that he plays favorites with his characters. For example, he confesses an "inclination of partiality" (16.6.2) to Sophia. In other words, he likes her better than a lot of his other inventions. The fact that the narrator can talk about how much he prefers some characters to other characters? That's a sign of how affectionate the tone of this novel is.
The narrator talks about these characters as though he knows them personally. He never describes any of them objectively (except maybe the forgettable "landladies" at every inn—those seem pretty abstract to us). And even the ones he doesn't like, such as Lady Bellaston or Mr. Blifil, never come across neutrally. The narrator's tone is emotional, even when he's being negative about the villains in the novel.
Still, even if the narrator talks about most of his characters like they are real people who he knows and loves, he doesn't deny their flaws. And that gets us to the other half of the tone of Tom Jones: the narrator is affectionate, but he's also sarcastic. So, for example, the narrator always calls Mr. Thwackum and Mr. Square "learned personages" (3.6.1), even though they are obviously both idiots.
Or, the narrator says that Bridget Allworthy speaks "with a voice sweet as the evening breeze of Boreas in the pleasant month of November" (1.8.5). Boreas is the Greek god of the north wind, and, unless you're in the southern hemisphere, where north = warm, and November = spring Boreas's name implies coldness and bitterness. So a voice that sounds like the north wind in November? That's going to be anything but "sweet."
The narrator often describes something in one way while strongly implying that it's the exact opposite. So while the narrator may like a lot of these characters, the overall tone of the novel still comes across as witty, darkly funny, and really sarcastic.