The Favourite button at the bottom right hand corner (a 'heart' icon in the latest windy) simply toggles viewing favourite locations on the screen.

This panel is called the 'Quick Menu' and you can configure it by clicking 'More layers'.

However the method to totally delete a Favourite remains the same as described by @dzuremar in the post above.

Also, please dont write in ALL CAPS, it is considered to be shouting - thank you.