Get a good larger boombox (portable) type system that is designed for such a purpose. Often with detachable speakers ! They are fairly costly, but some of the better companies make excellent systems that are contained in a sturdy housing.
Something along these lines. Many companies make larger decent systems.
http://www.jr.com/JRProductPage.process?Product=4146727
You might even take a look at the newer design Sony, and Bose "Wave" type systems on the market ! Great bass response !
I seriously doubt that you will find a system with many contained components that is actually completely "weatherproof". My guess would be that given the features of a full-fledged versatile stereo system with decent tuner, bass ported, CD format, and many inputs for other attachable features "quite weatherproof" just is not practical or affordable for a system that offers you versatility, power etc.
Get a larger portable system ! Don't leave it "outdoors". There's no need today to leave a system outdoors with nicer smaller portable systems self-contained systems that allow for additional speakers, detachable speakers, etc !
Other options of course are outdoor speakers, wireless speakers (which I've never been overly fond of)