I heard this on a BET television program.

Problem:
Many wonder whether “him” or “his” is correct in sentences such as this one.

Explanation:
The present participial phrase “singing with the choir” acts as an adjective to modify “him” in “I’m worried about him singing with the choir.” To prove this, we can remove the participial phrase and retain the sense of the sentence: “I’m worried about him.”

In contrast, if we replace “him” with “his” in the sentence, then “singing with the choir” may not be removed. That is, “I’m worried about his.” makes no sense; the possessive pronoun “his” requires the gerund phrase “singing with the choir” or another object.

Summarizing,

• “him” makes “singing with the choir” act as a present participial phrase;
• “his” makes “singing with the choir” act as a gerund phrase.

In other words, “him” and “his” are equally correct but have different effects.

Putting this summary in non-grammatical terms, we get the solution.

Solution:
Use “him” when you want to focus the attention on the person. Use “his” when you want to focus the attention on the action performed by the person.