Objects orbit the sun because of the sun's gravity, and Earth's gravity is weaker than the sun's gravitational pull. So why does the moon orbit the Earth instead of the sun?
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2 Answers
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The moon does orbit the sun but it also orbits the earth. But your assertion that the earth's gravity is weaker than the sun's is not universally true. If the sun's gravitational pull were greater than the earth's HERE on the earth, the sun would literally suck everything not attached to the earth's surface into itself. Clearly that's not happening.
Remember that Newton's Law of Gravitation says that the force is inversely proportional to the SQUARE of the distance. So while the sun does have a stronger gravitational pull, the distance that both we and the moon are at makes the earth's field dominate.
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The sun's gravity is strong but the the earth overwhelms the sun's gravity ,and the moon is in the in the place where the earth's gravity overwhelms the sun's, so in short the moon orbit the earth because it is in the place where earth's gravity overwhelms the sun's