grammar - In sentences with "too" and "enough" what word does the to-infinitive modify?

When a to-infinitive is used with words like "too" and "enough" what word does it modify? For example

The animal moves too quickly to be captured.

The bag is too heavy to lift.

He is scared enough to fire his gun.

At first I thought the to-infinitive modified the adjectives and adverbs quickly, heavy, and scared, but I got confused on later example sentences.

Bob is too eager to fight.

Bob is too eager to fight to wait.

It seems strange for two to-infinitives to modify an adjective at the same time, when it occurred to me that the to-infinitive may be modifying "too" instead. Is this true? In any case, "to wait" does not seem to modify the same way "to fight" does in the latter sentence, but I haven't found a good explanation on how a to-infinitive like "to wait" works with words like "too" and "enough" in dictionaries. Also, the first three sentences don't make much sense without "too" or "enough". "The animal moves quickly to be captured" has a much different meaning than "the animal moves too quickly to be captured."