"To be near" means "To be close to", or "To be with". Basically, the sentence "A popular guy with girls" focuses on the "popular", and ignores "with girls", which makes it rather confusing.Specifically, what I don't understand is 'to be near ...'.
Could you please put it another way?
According to your explanation, the preposition phrases 'with girls' and 'around the waist' are related with the whole noun phrases 'a popular guy' and 'a fat man', but not with the adjectives 'popular' and 'fat', isn't it?"A fat man around the waist," if it means anything, does not mean "a man who is fat around the waist." It could, instead, be taken to mean "a fat man who is near someone's waist." ("Around" can mean "nearby" or "close at hand," as in "My daughter is always around when I need her.")
Similarly, "a popular guy with girls" is ambiguous and might not mean "a guy popular with girls." It could mean "a popular guy who at the moment is accompanied by some girls."