If you search Google for Earl Weaver and platoons, a lot of good stuff comes up. There's a SABR article, a great Hardball Times piece, and an "online encyclopedia" that anyone can edit. The Internet is a treasure trove of information!
But if you were wondering just how committed Weaver (edit: or Joe Altobelli, who was actually the manager in 1984! In my defense, I was remembering the 1982 Topps Earl Weaver as a 1984 Topps card, so I didn't even check. My bad.) was to the idea of platooning, this should give you a pretty good idea:
|vs RHP as RHB||1758||1585||390||137|
|vs RHP as LHB||2816||2442||630||326|
|vs LHP as RHB||1597||1414||354||156|
|vs LHP as LHB||16||15||0||1|
The '84 Orioles won 85 games. They did not have a hit from a left-handed batter against a left-handed pitcher. Four switch-hitting starters and the rules of the American League helped out, for sure. Still, I'm not sure if we'll ever see a commitment to the platooning arts like that again.