Gear S3 Wifi is disabled when connected to mobile via BT

You can connect your Samsung Gear S3 device to a Wi-Fi network to use the Internet or share media files with other devices.

However, this feature is only available when the device is not connected to the mobile device via Bluetooth.
 

When connected to a mobile device via Bluetooth, Wi-Fi connection on Samsung Gear S3 is no longer needed as the device will use the data network of the connected mobile device instead.

Having two established connections in the device will increase battery consumption. Hence, Wi-Fi on Samsung Gear S3 is automatically disabled whenever it is connected to a mobile device.