Nothing to Worry about for CityBeat?
According to quotes from this Boston Globe story, the mainstream free newspapers started by the Tribune and Sun-Times in Chicago did not hurt the Alternative weeklies, at least according to the publisher of the Chicago Reader:

Jane Levine, publisher of the 32-year-old Chicago Reader, says the new Chicago tabloids have not eroded her readership. ''They're supposed to be youth-oriented publications, [but] they don't want to be alternative at all,'' says Levine. She adds that a healthy dose of ''attitude'' distinguishes the truly alternative press.

If the Enquirer weekly mimics every other similar "youth" targeted mainline paper, then CityBeat will survive with only a few revenue scrapes.