I have a MacBook air 2013. It has a 128GB M.2 SSD with 16GB of photos.
I'm trying to delete only the photos from my device.
I want all the photos to stay on ICloud but be gone from my MacBook
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The only way to remove the photos from your Mac is to sign-out of iCloud. This will keep the photos in iCloud but remove them, and all other iCloud-synced data, from the Mac.
iCloud is a syncing solution not an offline storage solution. It's designed to give you access to your data from any device that logged-into that iCloud account.
From Apple's iCloud page:
iCloud connects you and your Apple devices in amazing ways. It makes sure you always have the latest versions of your important information—like documents, photos, notes, and contacts—on whatever device you’re using. It lets you easily share photos, calendars, locations, and more with friends and family. It even helps you find your device if you lose it.
You could use an external storage device to store your photos and that will free-up your Air's HDD space.