Hi there! It would be better to say "I've already had a lot to eat." The present perfect here implies that in the past up to this moment you’ve had a lot to eat and so now, in the present, you're no longer hungry.

Otheriwse it would be best to say "I had a lot to eat (earlier, today, etc.)" without 'already,' but I believe the present perfect is a better answer.

B: Thanks I'll pass. I already had a lot to eat.