A move doesnt get stronger when a certain Pokemon uses it. The only thing that powers up moves is STAB,Items,Stat Modifiers, and Abilities. Delibird doesnt receive STAB so thats not it. It could be holding a item, or its ability Hustle, which raises Attack but lowers Accuracy. Maybe it had its Attack at a +1,+2,+3,+4,+5, or +6.
Delibird will only cause a huge amount of damage with Present is if it has a item to boost the damage, it has Stat Modifiers, or its Ability Hustle is in effect.