Q. My grandfather used to say "Little pitchers should be seen and not heard." Do you know what that means?
A. I can reconstruct a meaning, though I never heard it expressed exactly that way before.
Children used to be called “little pitchers” because their head and prominent ears looked like a container for liquids with projecting handles. [Remember Alfred E. Neuman?]
The standard saying was, "Little pitchers have big ears," meaning, "Watch out⎯the kid's listening! Be careful what you say!"
There was another saying, "Children should be seen and not heard." So it looks as if your grandfather combined the two.
"Little pitchers have big/wide ears" showed up in early collections of proverbs, such as John Heywood’s Proverbs (1546) and Nathan Bailey’s Dictionary of Proverbs (1721).
(substitute @ for AT above)