I'm full, so I can't eat any more.

Literal

Full-stomach [because-なので], already this more [potential-食べられない] eat-can't.

なので ('because, since') is the reasoning conjunction for a na-adjective or noun predicate — attaches the 'because' sense to 満腹だ. これ以上 ('any more than this') is a set phrase meaning 'beyond this point.' The potential 食べられない ('cannot eat') combines with これ以上 to mean 'can't eat any more.'