Outer lens diameter

I've seen many supposed wide angle lenses in my time. some with outer glass utilizing 77mm filters, and others using 55-62mm filters. My question is this: What is the real purpose of a wide angle lens with an outer diameter of 77mm compared to a wide angle lens with only a 52 or 55 mm diameter? I was under the impression the the rear lens glass and its maximum aperture dictated the amount of light coming into the lens, and not the size of the front glass. If this is the case, why have a lens that has  77mm outer glass? I'm not a pro, not even closes. I was always curious about this. Please, no flaming, it's a simple question.

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Sony NEX 7, Sony A550