SWA isn't flying out of Newark any time soon. In fact, the EWR that you're seeing comes from the ATA codeshare. You'll also see destination listings for BOS, LGA, DCA, MSP, SFO, HNL, and OGG.
Some of the codeshares will be going away as ATA retrenches into its profitable west coast-hawaii routes. This includes EWR, MSP, and a few others that I don't recall off hand.