Final answer:
Both "I prefer going out on the weekend." and "I prefer to go out on the weekend." are correct in English. They are examples of using gerunds and infinitives after the verb 'prefer', which can often be used interchangeably.
Step-by-step explanation:
The correct usage in English when expressing personal preference. Both sentences "I prefer going out on the weekend." and "I prefer to go out on the weekend." are grammatically correct. In English, the preference of using a gerund (going) or an infinitive (to go) after the verb 'prefer' can depend on the context, but in this case, both forms express the same meaning and are interchangeable.
In some examples, the choice between a gerund and an infinitive can convey subtle differences in meaning or indicate a preference resulting from regional English variations. For instance, British English speakers tend to use gerunds more frequently, while American English speakers might favor infinitives in certain contexts. However, these preferences are not strict rules and are more about usage conventions than correctness.