Hi TinyBarb65,
Thanks for coming to Apple Support Communities for help today.
You will have to delete the messages you no longer want. However, you may be able to make more storage available in iCloud by following the suggestions found here: Manage your iCloud storage
"Make more space available in iCloud
If you run out of iCloud storage, your device won’t back up to iCloud, new photos and videos won't upload to iCloud Photos, and iCloud Drive, other iCloud apps, and messages won't stay up to date across your devices. And you also won't be able to send or receive emails with your iCloud email address.
You can free up storage in iCloud by deleting content that you're not using:
Before you delete anything, you might want to archive or make copies of the information that you store in iCloud."
Have a fantastic day!