Why would your radiator suck up antifreeze from the over flow?

If there is no leak visible so you can see antifreeze under the parked car, you probably have a head gasket going bad. You may have some signs of steam in your exhaust, or at least a sweet smell coming from the exhaust. You should have a compression test done on your engine.

That is exactly what the overflow reservoir is for. When the engine is hot, excess coolant goes into the overflow tank, as the engine cools,it draws coolant back into the radiator.