This phrase, originating from SmashBoards, was originally used to describe the Metroid series's Ridley, a space pirate who is commonly requested to be a character in Smash. Those who oppose the idea of Ridley being a playable character commonly use the argument that "Ridley is TOO BIG", in reference to Ridley's large size and proportions.
This caused a worldwide phenomenon in which everything and everyone is referred to as "TOO BIG", with several characters being considered too big. This phrase quickly grew into a joke that almost nobody takes seriously, with a few individuals taking it seriously. The meme is now pretty much dead, but that's a good thing since Ridley will finally be playable in Smash. Although hilariously enough, Ultimate's actually referenced the meme twice, both with the tagline "Ridley hits the big time" and Ridley's taunt where he just stands straight up.
When it was revealed that Ridley wasn't in Brawl, people were disappointed. They started asking why their god Sakurai had forsaken them. But some users saw the light, and they explained to us why Ridley wasn't in Brawl. "RIDLEY'S TOO BIG!" Contrary to popular belief, this argument was not started by Shokio (see below), but actually during the pre-Brawl speculation.
Since then, Ridley supporters have united as Space Pirates all over the internet to begin a crusade of "No, Ridley's not too big..." for six years. To this day, we still argue about Ridley's size. People who hate Ridley have become known as "Too Bigots," even if they don't think that size is an issue (hint: they usually do).
This argument was resurrected on July 20, 2013 when YouTube user Shokio uploaded a video  where he said that Ridley was too big in response to Smash Bros. speculation (in that video, in addition to providing incorrect evidence, such as stating that Ridley is in Metroid Prime 2, and that Mecha Ridley is fought in Fusion, among other errors, he also said that Miis don't belong). While he would later said he was joking (hint: he wasn't), this video made Shokio the face of the "Too Bigots."
And Then It Actually Happens...
And then Sakurai went and revealed that part of the reason Ridley wasn't playable was because of scaling ruining his character, or something. But of course no one's going to say that it's still ridiculous even when Sakurai says it, because this board lives to please Sakurai. And it has nothing to do with the fact that Sakurai's holding a gun to my head right now and OHARCEUSHELPME or anything, because that would be ridiculous, and ILOVEYOUDADDYSAKURAI.
Ridley was shrunk down, meaning Sakurai's a big liar, and put Ridley in Smash 5.