Found about 330 “at”s in the text, and these are some of them, along with GPT’s explanations.

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* The odd superstitions touched upon were all prevalent among children and slaves in the West at the period of this story—that is to say, thirty or forty years ago.

GPT:
Use 'at' for specific points in time, like a clock, a day, a week, or a celebration.

In formal or literary contexts, 'at' can also refer to a period, era, or stage, treating it as a conceptual point on a timeline, for example: 'at the period of this story'.

Even if the period is long, 'at' shows the time when something happened.

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* So she lifted up her voice at an angle calculated for distance and shouted: “Y-o-u-u TOM!

So they stood, each with a foot placed at an angle as a brace, and both shoving with might and main, and glowering at each other with hate.

GPT:
In phrases like 'at an angle', 'at' shows a geometric position or orientation, not a physical location.

It specifies the angle or tilt of something, for example: voice lifted at an angle means the direction of the voice, foot placed at an angle means the foot's position or tilt.

This use of 'at' is different from everyday uses like places, activities, or addresses.

Think of it as: 'at' marks a specific point on a scale or in a position, here referring to the angle.

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In 'glowering at each other', at is a preposition showing the target of the angry look.

The verb glower is usually followed by at when specifying who or what the anger is directed toward.

It works like other verbs of looking, such as stare at or look at.

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* Look at your hands.

* And look at your mouth.

GPT:
In 'look at your hands', 'at your hands' is a prepositional phrase, with 'at' functioning as a genuine preposition that heads the PP.
The verb 'look' selects (subcategorizes for) a PP headed by 'at' when it takes an object of perception.
Although 'at' is lexically dependent on 'look', it retains its independent prepositional meaning, expressing direction of attention.
Therefore, 'look at' is not a phrasal verb, and 'your hands' is not a direct object but the complement of the preposition 'at'.

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* The more Tom stared at the splendid marvel, the higher he turned up his nose at his finery and the shabbier and shabbier his own outfit seemed to him to grow.

GPT:
stare is a transitive verb that normally takes the preposition at when it has an object.
She stared at the painting.

Contrast with similar verbs:
Some verbs look similar but behave differently:

look → look at
glance → glance at
gaze → gaze at
watch → no preposition (watch the movie)

So stare patterns with look / gaze, not with watch.

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* The phrase 'turn up one’s nose at' is an idiom meaning to show disdain or contempt for something.
* In this idiom, 'at' is inseparable; removing it makes the expression ungrammatical.
* It is still used today, especially in formal or literary contexts.
* In casual speech, people often replace it with simpler alternatives like 'look down on' or 'snub'.

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