When I connected the Sony Xperia ZR smart phone to the Sony Bravia TV via the USB port, the TV did not display any folders from the SD Card of the phone. After a while, realized that the phone was connected to the TV USB port in MTP (Media Transfer Protocol) mode.
To display the folders from the phone’s SD Card on the TV, you need to make sure that the phone’s USB Connectivity mode is MSC (Mass Storage Mode).
To set the phone to Mass Storage Mode (MSC) mode, go to Settings -> Xperia Connectivity -> USB Connectivity -> USB Connection Mode and select Mass storage mode (MSC).
Note that after you are done, disconnect the phone from the TV and then re-select Media Transfer Protocol (MTP) mode.
In Mass Storage mode, you can select any media file recognized by the Sony Bravia TV and play it. Use this to play music, movies or even your photos stored on the phone.