With open enrollment season in swing, many employees may notice something conspicuously missing from their benefits menu — coverage of GLP-1 drugs for weight loss.

More companies are dropping coverage completely or offering employees less generous payouts. In some cases, they're shifting to a different model altogether — offering employees a consolation prize of sorts — access to a weight management program through a third party.

Coverage of these drugs for weight loss is pricey for employers — typically costing in the mid-$500s to mid-$600s per user monthly. Some companies say whatever the price, covering the drugs is worth it based on employee health. "We spend about $250 million or more on GLPs, and that's up from zero" four or five years ago, Bank of America CEO Brian Moynihan told CNBC's Andrew Ross Sorkin in August. "We see a great impact on the employees. ... Believe me, we're pounding everybody on price and trying to get as cheap [as possible].…