Why would a station affiliate with the CBS Sports Network? Because CBS is going to make this network becomes a major player.
They have Jim Rome on the schedule, who had been one of the nation's top syndicated sports radio programs before joining CBS. They're probably going to get a lot of major sports events which CBS will buy. Right now ESPN has the big ones, Super Bowl, World Series, MLB playoffs, etc. But you can be sure that CBS will use the clout of their TV network to negotiate deals for CBS Radio Sports, stealing them from ESPN.
Remember that CBS now owns ten FM Sports stations in large markets...
New York
Dallas
Philadelphia
Washington
Atlanta
Boston
Detroit
Tampa
Pittsburgh
Baltimore
and plenty of AM stations across the country carrying all or part of the CBS Sports line up. So for their own O&Os, they're committed to making the CBS Sports Radio Network as good as ESPN. And all the AM Sports stations owned by Cumulus are also now CBS Sports affiliates, since Cumulus is a partner with CBS in this new venture.
To say WEAV will be airing an inferior product with CBS instead of ESPN is to misunderstand how committed CBS is to this new network. Meanwhile, it's perfectly logical to run ESPN on 101.3 when local hosts aren't on, and to run CBS on 960.