Before I get to the 1983 cards, I was able to find out a little more about Big League Collectibles.
I got this card in the mail yesterday and it has some ordering information. You see that the company was based in Canal Winchester, Ohio. That gave me a little more to search with and led me to an Ebay page of a listing for a Diamond Classic set.
The listing says the following:
~ Issued by Big League Collectibles, Inc., in 1982 ~
Starting in 1982 our family planned, produced, packaged and promoted 4 numbered, limited edition card sets under our company name, Big League Collectibles, Inc. We were based first in Canal Winchester, Ohio, and later New Gloucester, Maine.
Each card was produced by hand painting in colored oils a postcard size black & white photograph of a popular ballplayer. A brief biography together with statistics was added. The cards were manufactured on sturdy 6-ply card stock (similar to the 1933-56 Goudey, pre-1957 Topps, Gum Inc., etc.). Card size is 2-1/2" by 3-3/4" - same size as the popular 1953-55 Bowman baseball cards.
The ebay sellers user name is The Baseball Hobbyist and Gram. Their seller page has a little more information:
In 1957 we started on a long journey of involvement with baseball-oriented collectibles. From buying one- and 5-cent packs of cards (with gum) to eventually publishing our own card sets, it has been a most interesting hobby. We hope to remain involved through Ebay for years to come. -- Steve & Linda
So it looks like Big League Collectibles was a mom and pop operation that went from collector to producer. They sold out all four of their sets, but then quit producing cards. I sent them a message through eBay with some questions about their venture and hope to post their responses on Monday.
Big League Collectible's second release in 1983 was a continuation of 1982s Diamond Classics. The set size is again 55 cards and they are numbered from 56 - 110, picking up where '82 set left off. The set was again limited to a print run of 10,000.
The 1983 set was much more Cub-friendly. with six of the 55 players being Cubs.
The six Cubs are Ernie Banks, Guy Bush, Charlie Grimm, Billy Herman, Bill Nicholson, and Riggs Stephenson.