The two most popular sports in Iran are football and volleyball, with baseball being the least popular.
The structure with + noun + present participle is grammatically correct used in written English, especially in formal English.
According to The Free Dictionary, the preposition "with" is also used as a function word to specify an additional circumstance or condition such as "we climbed the hill, with Jeff following behind".
The present participle after the noun basewall gives the sense of the past tense as the verb mentioned earlier is in the past. So, instead of saying "and Jeff followed behind", we can say " with Jeff following behind".
His two sons are engineers and the third one is a doctor. I think we can also say ",His two sons are engineers, with the third one being a doctor.
However, to avoid any ambiguity, we can use while, whereas, or and instead of with in such sentences.