In the Name of God, the Compassionate, the Merciful.
Hi!
Doctor: Ah … excellent. No sore throat. In that case, nothing’s the matter with you.
Man: No, nothing at all. I just wanted to get a check-up. Is it possible to get a check-up now?
Doctor: Hah, well, I can give you a quick check-up. It is possible, yes, but … let’s start by checking your height. How tall are you? ←
What does “check” mean here?
Why “check” and not “measure”?
Thank you
Yes, in this case it means measure. Whether they use measure or check is just a choice of words.
As part of a vocabulary lesson, I think they are reinforcing the word “check”. They are talking about a check-up. During a checkup you check things, like height, weight, blood pressure, etc.
Thank you so much, NearlyNapping 
Very nice.
Strictly speaking, I think “measure” is the better word. Sometimes they might just say “get your height”, but they aren’t actually checking your height to see if it’s okay as they do when checking your blood pressure.
[I’m sorry, sir, but you’re too tall. We’re going to have to …]
But, as NN said, they’re talking about checking things in general, so they just used it for height.
Thank you so much, Arinker
Very nice.