What is the omitted subject of 'eating with your brother' in 'the big guy eating with your brother'?

Solution 1:

Both big and eating with your brother modify guy, the head of the NP. This is a coordination of pre- and post-head modifiers.

We can't have

* Who's big guy?

anymore than we can have

* Who's guy eating with your brother?

Thus the the would appear twice without the coordination.

Who's the big guy, the guy eating with your brother?

Sometimes it's not possible to linearly cut up sentences in order to understand the relation of one part to the others.

More importantly, the subject in this example is not "omitted" as there is no way to put it into the sentence even if we wanted to, gerund-participials in modifier function in NPs cannot contain an overt subject. Were we to extract it and re-write we might come up with something like:

the guy who eats with your brother

or

the guy who is eating with your brother

Solution 2:

(1) Who's the big guy [ ___ eating with your brother]?

eating with your brother is a reduced relative clause. The sentence that includes the implied subject is

“Who's the big guy that/who is eating with your brother.

“with your brother” = {preposition + NP}, i.e. a prepositional modifier.