according to Junius, is from the Latin pampinus, French pampre (vine-tendril). Hence Milton-
Where any row Of fruit-trees, over-woody, reached too far Their pampered boughs, and needed hands to check Fruitless embraces.
Paradise Lost, v. 214.
The Italian pamberato (well-fed) is a compound of pane (bread) and bere (drink).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894