ولد مريض ضعيف = A sick, weak boy.
In Arabic, the adjective must follow the subject/noun in definition, they're both definite, or both indefinite, that's why since the subject "boy" is indefinite, all the indefinite nouns after it are adjectives.
In the first sentence, the "boy" was definite, so since the word "weak" was indefinite, it became the predicate, not an adjective.
For the first sentence:
الولد = definite.
المريض = also definite = adjective for "الولد".
ضعيف = indefinite = predicate.
For the second senence:
ولد = indefinite.
مريض = also indefinite = adjective for "ولد".
ضعيف = also indefinite = adjective for "ولد".