I have a 2001 Malibu (3.1L, V6). The engine light just came on today, but I'm quite sure there's nothing wrong with the motor as I had it overhauled this spring. I think the battery may be weak. Is it possible for the engine light to come on as a result of a weak battery?

A weak battery can cause the light to come on but that isn't the most likely of causes.
The light may have come on due to a loose gas cap, a faulty evap system solenoid, even poorly maintained cooling systems can cause DTC's to store.
If you're not experiencing any dramatic symptoms, it could go out on it's own. It will just take a little while.

Agree with Rich; drive the vehicle for a week or so. If the light doesn't go out after that time, then get a scan done to determine the cause.