I like bigger hats, since they protect against the sun better. Small hats with barely any brim don’t really serve much of a purpose.
Perhaps bigger hats have also become more popular because they are a bigger statement against assimilation. A small hat suggests you’re trying to be lower profile. A big hat suggests you don’t care about sticking out with your huge headwear, since you’re proud to be a frum Jew and totally out of step with American popular culture. The more loud and distinctive to Jews the hat is, the better it is in terms of assimilation and group pride. (I guess we can’t take that principle too far — otherwise we’d be wearing gigantic top hats with huge neon yellow stars of David all over them.)
Also, the Lubavitcher Rebbe’s use of a big wide hat for decades may have influenced even non-chassidim to adopt similarly full-sized hats. Reportedly, asked by a chassid whether the chassid should wear a traditional chassidic-style hat according to his specific local minhagim, the Lubavitcher Rebbe replied that no one nowadays is going to be impressed with such a hat — just wear a Borsalino (a basic dressy hat that at the time (a few decades ago) was the mark of a respectable middle-class person in America).