A reader points me towards a post by David Crystal looking into why we say 'my apologies' in the plural. A while ago I asked the same question about 'hopes'. Crystal suggests 'a pragmatic explanation, focussing on the "century of manners":
The 18th century strikes me as being the time when people might have felt one apology wasn't enough, so they really went in for pluralizing it.
(Thanks: CC.)