Likutei Moharan 58:6/ליקוטי מוהר"ן נ״ח:ו׳

16. The reason that the sage supplies the aforementioned “double bread” is that through his worthiness he merited his neighbor’s portion as well. As our Sages, of blessed memory, said: If he is worthy, he takes his own portion and that of his neighbor (Chagigah 15a). Thus, when the day of Shabbat arrives and his NeFeSh (soul) is encompassed in ShaBbaT, in the aspect of “for on that [day] ShaVaT va’yeNaFaSh (He ceased working and He rested)” (Exodus 31:17), [the sage] then gives “double bread” to the day of Shabbat, as explained above.