Wiktionary
a. filled to satiety
Usage examples of "full up".
I can tell by the look of you that you're just full up with speeches, but they'll keep.
They travel nearly all over it, and there is no town out of which they do not go full up of meat and drink, as the saying is, and with a real, at least, in money, and they come off at the end of their travels with more than a hundred crowns saved, which, changed into gold, they smuggle out of the kingdom either in the hollow of their staves or in the patches of their pilgrim's cloaks or by some device of their own, and carry to their own country in spite of the guards at the posts and passes where they are searched.
Sickness and trouble: that's what Ethan's had his plate full up with, ever since the very first helping.