From Longman Dictionary of Contemporary Englishheavy breatherˌheavy ˈbreather noun [countable]  SCCa man who telephones a woman and does not speak, but breathes loudly, in order to get sexual pleasure —heavy breathing noun [uncountable]
                                                    
                                                Examples from the Corpus
heavy breather• She had reduced the voice to something on the same level of annoyance as a heavy breather. 
