Equinox isn’t afraid of weight-loss drugs. Really.

Upscale fitness chain Equinox seemed to be throwing in the towel. In January, gym members in select markets started receiving messages about a new club benefit: a training program that was, according to Equinox, a “one-of-a-kind approach to weight loss with GLP-1.” Coming soon after WeightWatchers’s launch of a telehealth program to prescribe weight-loss drugs for its members last December, Equinox’s so-called GLP-1 training “protocol” looked like another admission that diet and exercise...