In a comment, Hot Licks wrote:

> It is, of course, a Trumpism to a large degree.  "Big league", in the US, refers primarily to "major league" baseball teams and games, or at least to adult baseball, as opposed to "Little League" children's baseball.  The idiom has been detached from that meaning over the years, though, and now might be used to refer, eg, to a company which has grown to the point that it can compete with others in a national market.  Trump abuses it to a degree to simply mean "big", or "bigly" (sic), as you suggest.