2006I was asked by one of my students the other day about the following structure:
1) "I like many sports, (with) football being my favourite."
You could add 'with' before "football". (see below)
I wonder if anyone could shed some light on the grammatical significance of the continuous verb form 'being' used here, and how it corresponds with other elements in the sentence. (my underlining)
When one replaces the verb with the copula 'is', the resultant effect is a more distanced relationship between the two clauses. I wouldn't argue with that, except that you can't replace "being" with "is" because there is a comma there, not a semicolon or period.
Additionally, one could not say the reverse:
2) "Football being my favourite, I like many sports." I think you can say that. And especially if you add "With" at the beginning of the sentence, you definitely can say it.
Is there a particular term for this structure? I assume that you mean sentence 1, the one your student asked you about.
All I can say is that the sentence starts with an independent clause and is followed by a dependent clause adding more information. Sentence 2 reverses the clause order.