Will ATC proactively route traffic around bad weather?
Yes, ATC will reroute flights that are operating on Instrument Flight Rules (IFR).
There are lots of videos of flights getting routed around severe weather floating around on the internet! Atlanta is a great example, as is Memphis, FedEx's hub.
In addition, NASA is working on a product called Dynamic Weather Routes that will help controllers be smarter about amending planned or unplanned weather reroutes.
Sort of, for aircraft operating VFR.
VFR flights that are talking to ATC may get advisories about weather and suggested headings from the controller. I've received notifications about things like 'moderate to heavy precipitation 5-10 miles ahead' many times when operating on VFR flight following.