What are the sources that suggest to sing each stanza of Shalom Aleichem on Friday night only once as opposed to repeating them 3 times?
The Yalkut Yosef (1:268:25) brought here writes:
נהגו לומר בליל שבת פזמון ''שלום עליכם'', ויש הנוהגים לכפול כל בית ג' פעמים, אך אם ממהר ללימודו, וכיוצא בזה, אין צריך לכפול.
"There are those who are accustomed to say Shalom Aleichem on shabbos night, and others have the custom to repeat it three times. However, if you must go quickly to learn or the like then you don't need to repeat it." Seemingly, the custom is really to only say it once.