They were actually on the same sofa, for Mrs. Musgrove had most readily made room for him: they were divided only by Mrs. Musgrove. It was no insignificant barrier, indeed. Mrs. Musgrove was of a comfortable, substantial size, infinitely more fitted by nature to express good cheer and good humour, than tenderness and sentiment; and while the agitations of Anne's slender form, and pensive face, may be considered as very completely screened, Captain Wentworth should be allowed some credit for the self-command with which he attended to her large fat sighings over the destiny of a son, whom alive nobody had cared for.

IMO that refers to the idea that connects plumpness (or fatness) with joviality and good-humour; after all, a fat person is someone who is supposed to enjoy the earthy pleasures of life like food. Think of popular characters like Friar Tuck in Robin Hood Tales, or Falstaff, or even the common image of Santa Claus (although I suppose that JA would not have known the last)