The case
It became the shorthand for an over-earnest acceptance speech within a week. But the speech itself, on the 1985 Oscar telecast, is a slightly different sentence with a different rhythm: "you like me, right now, you like me."
The word "really" was added by the impressions, most famously in the years of parody that followed. Field has spent decades explaining that she never said it.
Why our brains do this
Parody tightens a quote into its funniest form, and the funniest form is the one that gets repeated.
Sources: Wikipedia — Sally Field · Wikipedia — False memory: the Mandela effect