Learn Dutch: Ik ben wezen roeien en ik heb me goed vermaakt.

While ik heb geroeid just means "I rowed," ik ben wezen roeien specifically means "I went rowing." Dutch uses the combination of zijn (here ben) + wezen + an activity verb to describe an outing that you have completed and returned from.

What exactly is the word wezen doing here?

Wezen is an alternative infinitive form of zijn (to be). In this specific "action perfect" structure, it takes the place of the past participle geweest. Dutch grammar requires two infinitives together at the end of the clause here, so we use wezen roeien instead of a past participle.

Why is there a me in the second half of the sentence?

It is there because the verb zich vermaken (to enjoy oneself / have a good time) is a reflexive verb. Since the subject is ik, you must include the matching reflexive pronoun me (myself). Literally, you are saying "I have entertained myself well."

Could I translate "I went rowing" using the simple past, like ik ging roeien?

Yes, ik ging roeien is grammatically correct. However, in everyday spoken Dutch, people heavily prefer the present perfect tense (ik ben wezen roeien) to talk about completed casual activities and outings.