Put a multimeter between one of the battery clamps and the terminal on the battery, set to amps. Leave it sit connected for a half an hour or so then check the reading. You would expect it to draw some small number of milliamps with the ignition off. Don't try to start it or even turn on lights or anything or you could blow the fouse or the meter itself.
Let us know how much current it's drawing. 3 weeks is not absolutely terrible but it isn't fantastic either.