I have not played an Eberron campaign very much, but I have read through the 4th ed. campaign guide. I may be wrong, but I don't believe the idea is that everyone knows a little magic, but rather that magic is widespread, though not often very deep. Magic is used for the utility of society.
In other words, it's like there are a lot of "magic workers" out in the world, who don't know a lot of magic, but have learned one particular thing in their chosen industry, like magically raising horses so that they can run faster for longer distances without getting tired, or magically controlling elemental forces to power airships, or using magic to teleport messages from one city to another, thus setting up a mail system.
These magic workers aren't powerful mages or wizards, they just know their one thing, and that's how industry is created in society. It's basically the industrial revolution, but with magic instead of technology. There are powerful wizards and other magic casters out in the world whose knowledge is both deep and wide, but they are much more few and far between. The magic workers know just enough to do their jobs.
But there are still plenty of people who don't know any magic at all. Fighters, thieves, politicians, etc., who just rely on the services of the "magic workers" and the various industries in their day-to-day lives.
So if I understand your question correctly, you don't need to give everyone magical ability in an Eberron world. Also, WOTC released some Eberron playtest material that might help you out:
http://dnd.wizards.com/articles/unearthed-arcana/unearthed-arcana-eberron