Why do we say, "No thank you, I have had elegant sufficiency," when asked if we want more to eat?

My wife often comes out with the complete phrase "No thank you, I have had an elegant sufficiency and anymore would have been a superfluous indulgence."
I on the other hand just burp and pass out

The phrase seems to be a variation on a polite rejoinder that was once quite widely known and is still around. A host might ask if you have had enough to eat. Rather than just say that you had had enough, being fearful that so bald a statement might be taken as unrefined or ill-bred, you might instead say, “I’ve had an elegant sufficiency”. This presumably has its origin in some catch phrase old enough that it has had time to disseminate widely, since I’ve seen examples from Scotland, Ireland, Wales, Australia, and the USA. A possible source is a poem called Spring by James Thomson, dating from the middle of the eighteenth century, very widely quoted during that century and the following one:

An elegant sufficiency, content,
Retirement, rural quiet, friendship, books,
Ease and alternate labor, useful life,
Progressive virtue, and approving Heaven;
These are the matchless joys of virtuous love.