Hi!
I am translating a book from English by John Bridges, How to be a Gentleman, full of wise and strange tips.
What does this mean:
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In the workout room, a gentleman does not hog the weights.
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Has it something to do with "showing off" ?

Hogging something is keeping it for yourself and not letting others use it. The passage means that a gentleman would let other people have a turn with the weights rather than holding on to them the whole time he is there.

Oh, thank you!

Of course, a true gentleman does not 'work out' ! He gets his exercise elsewhere.