Some historians argue that the Quartering Act of 1774, which

I assume you forgot to add the question stem. That makes me sweat in a couple of seconds

This is WEAKEN question, therefore determining the conclusion is key.

Fact: The Quartering Act of 1977 permitted British soldiers to demand housing in colonist occupied dwellings
Conclusion: The Act was the key cause of the American Revolution

To weaken the conclusion, we need to show: there was another factor that caused the American Revolution. ==> Therefore, we cannot conclude the Quartering Act of 1977 was the key cause of the American Revolution.

ANALYZE EACH ANSWER

A The Quartering Act of 1774 was bitterly protested, and can be linked to multiple colonist outbursts.
Wrong. It strengthens the conclusion.

B The unpopularity of the Quartering Act was overshadowed by that of the Massachusetts Government Act of 1774, which sparked outrage by restricting the colonists' right to assembly.
Correct. The Quartering Act was actually not popular. Actually, there was another Act (the M.G Act of 1774) which is the main reason of American Revolution.

C Many colonists refused to grant British soldiers entry to their homes, in protest of the Quartering Act of 1774's provisions.
Wrong. It strengthens the conclusion.

D The number of colonists enrolled in militias greatly increased in the months following the Quartering Act of 1774.
Wrong. Out of scope.

E When drafting the Quartering Act of 1774, some British officials voiced concerns about the potential colonial reaction.
Wrong. Out of scope. It does not weaken / strengthen at all.