"upper reaches of a profession or pursuit," c.1910 from vaudeville slang; the phrase was common in colloquial use late 19c.-early 20c. in a broad range of senses: "party, shindig, fun, frolic."
Important; notable: My book was big-time (1910+)
Very much; totally: Where does it say that a congressman has the right to be on the take big time?/ It sticks big-time to any smooth surface (1970s+ Army)
[ultimately fr the outdated theater sense]