why is there a word "way" in those sentences?
"Did she used to be way more cute?" and "She used to be way more fun"

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"Way" is slang for "much" or "a lot." "Did she used to be a lot cuter?" "She used to be much more fun."

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Gertie, thanks a lot!

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In North America, "much". EX: "I was cycling way too fast"
In the U.S., "extremely; really (used for emphasis)". EX: "The guys behind the bar were way cool"

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adverb (informal): 1. at or to a considerable distance or extent; far (used before an adverb or preposition for emphasis). EXAMPLE: "His understanding of what constitutes as good writing is way off base."