World Clock Deluxe uses the web proxy settings in the Network pane of System Settings (macOS 13 or later) or System Preferences (macOS 12 or earlier) when retrieving weather reports from the Internet or checking for updates.
If your network uses an HTTP proxy, make sure the settings in the Network pane of System Settings (macOS 13 or later) or System Preferences (macOS 12 or earlier) are correct.